With the Eyrie sitting atop the tallest mountain in the Vale, the Giant's Lance, it often got rather cold in the castle. But with winter setting in it was getting unbearable, and the inhabitants were forced to move to the Gates of the Moon, a nearby castle sitting at the base of the Giant's Lance. Oddly enough, this was the first true winter Jasper had experienced in Westeros, and it was three years after Mya had come to the Eyrie.
The seasons were something that confused Jasper immensely. While he understood that it had something to do with magic, he had no idea how it could stay in summer or winter for years at a time. According to Maester Colemon, it was the result of an ancient war with the Others, a race of necromancers that had attempted to take over Westeros, well before the unification. It took an alliance between the Children of the Forest (which sounded surprisingly like House Elves) and the First Men to push the Others out of the North. Apparently, this led to the construction of The Wall and the founding of the Night's Watch.
But the war was long and brutal, and while no one knew the specific magic involved, it was during this time that the Children accomplished feats of magic that have never been replicated since. During the First Men's invasion of Westeros, the Children somehow managed to completely destroy the Arm of Dorne. They shattered it into pieces, erasing the only land bridge between Westeros and Essos and creating a new chain of islands in the process, the Stepstones. This ultimately stranded the First Men in Westeros and ended the brief war between the two races. It was also the Children that altered the turning of the seasons. Many theorized that it was to lock the world in a state of summer, robbing the Others of the cold they used to power their magic. The effectiveness of this is unknown, but the Alliance was later able to push the Others deep into the North and lock them behind The Wall.
Unfortunately, the weather wasn't the only thing on Jasper's mind. Ever since they had moved to the Gates things had been rather tense. News had reached the Vale that the crown prince, Rhaegar Targaryen, had kidnapped Ned's sister, Lyanna Stark. Ned's brother and father had both apparently been arrested shortly thereafter, when they demanded Lyanna's safe return. Effectively, with this one action, House Targaryen had just taken the entirety of House Stark hostage, apart from Ned, who was still in the Vale.
Unsurprisingly, all the Northern houses were outraged by this, and now several of them were preparing to march on the Neck and make their way to the capital. Farther south, fighting had already broken out in the Stormlands, as Lyanna had long been betrothed to their liege, and it seemed that the Riverlands may soon join them in open rebellion. While the Reach and Dorne were quick to come to the King's defense, several kingdoms were still undecided, and lines were suddenly being drawn across all of Westeros.
Amid all this turmoil, Rowena had fallen ill and the maesters didn't know how to treat it. Jasper suspected it was pneumonia, but without access to potions, his magic was only suited for treating broken bones and stab wounds. Not to mention that his experience with healing spells was rather limited. He knew that it could be fatal though, so he urged Mya to spend as much time with her as possible. It was the first time in either of his lives that he truly hated giving up his muggle education. He kept telling himself that if only he had paid a little more attention in school, if only he listened that much more, he could have saved her from this. Instead, he found himself praying to every deity he could think of to spare her.
Between the two of them Rowena was hardly ever alone, and despite her comments about needless fussing, she seemed to love their time together. He snuck into the kitchens every day to make her breakfast and he kept her company throughout the mornings, talking to her endlessly about anything he could think of. From the gossip among the castle staff to the flowers Mya had found growing beside the stables. Even the news of the fighting scattered across Westeros. He refused to let her feel cut off from them, especially when it could be the last days they spent together. Mya was much the same, always bringing flowers and books and spending hours with their mother, daily. In the end though, Jasper was helpless to save her from whatever sickness she had, and he was forced to simply watch as her health continued to deteriorate. While his magic was able to ease her pain, it did nothing to stop the physical effects. She managed to hold out for a fortnight, but by then her body was just too weak to continue, and she died in her sleep.
Jasper had truly come to see her as his mother, and he had developed more of a relationship with her, than almost anyone in his last life. Her passing pushed him into a deep depression that only Mya was able to bring him out of. It was something that she noticed right away, and she did her best to keep him distracted and she refused to let him just sit in his room and brood. At nine, she may not have understood everything that had happened, but she knew he was sad and struggling. She dragged him around to play with her and explore the grounds, she pushed him into apple picking and pony riding. Anything to keep him from thinking too much and feeling the hurt she knew was inside.
But it wasn't long before his sadness was replaced by a righteous fury. She was home, she was supposed to be safe and protected, and all it did was mean she died from the comfort of her bed. He refused to let this stand; he was a wizard for Merlin's sake! No one else will get sick and die over a bloody chill, not when it's something he can prevent. He threw himself into working on the Eyrie, frequently apparating to the mountain so he could enchant the castle. It was mostly small things, but he found carving the runes to be calming, and he ended up creating several projects to drag out the work.
He added heating charms to the walls and floors to reduce the constant chill. What little bit of plumbing they had, was carefully charmed to never freeze or break. He even warded all the windows to prevent heavy gusts of wind, a tricky array to design, because it still had to allow for objects and light breezes to pass through.
Unfortunately, without the constant wind, the castle's sewage system (A simple set of tunnels that ran to the base of the mountain) began to smell far more noticeably, so vanishing charms were quickly worked into that as well. He made sure the guard towers and barracks were warded with the same set up as the castle, although the courtyard was left untouched to make the magic less obvious.
The only really blatant displays of magic he did was build a well next to the godswood, carefully charmed to never freeze or run out of water, and add a set of stairs within the godswood itself. The stairs led down to a "previously undiscovered" hot spring, in an underground cavern he had created. The cavern's ceiling was covered with various types of glowing crystals, each filling the chamber with a soft light. He figured the whole thing would be attributed to the Old Gods anyway but covered the stairs and well in runes used by the First Men to push the assumption.
After his recreation of the godswood and the reaction it gave in the Eyrie, Jasper had started researching the different religions in Westeros. When the smallfolk were given a choice, most found the Old Gods more to their liking than the Faith of the Seven or the Red God. There was no need for septons or holy texts, and no need of monetary donations to keep the Gods happy. You didn't have to undergo any sort of rite or service, all you had to do was say your prayers to the weirwood tree and that was it. And if the gods wished to speak to someone, then the wind would rustle the leaves of the tree. Even at a wedding, anyone could perform the ceremony, although an official of some sort had to be present make things legitimate. In fact, several of the things that the Old Gods condemned were already frowned upon in Westeros, such as kinslaying, rape, incest, and slavery.
And it wasn't just the smallfolk that preferred the Old Gods. Many lords found the Faith too restrictive, particularly for their views on prostitution, bastardry, and gambling. But the Faith had a presence in Westeros since the Andal Invasion, and many people feared slighting the gods, be them real or imagined. Not to mention that while the nobles may care little for the Faith, few could deny the influence and power that they wielded. Few dared to displease the church, and those that did were always sure to pay their price in gold, lest they suffer the consequences. With only the North fully supporting the Old Gods, it was the Faith that pushed the feelings of superiority in the South. They had long since viewed the North as a threat to their teachings, and many septons preached of the barbaric northmen and their unholy traditions.
The only other religion in Westeros was the worshippers of the Drowned God, which was almost exclusively found in the Iron Isles and was largely considered to be a state-driven cult by most mainlanders. From what little he could find on it he was forced to agree. With it regularly encouraging ritual sacrifice, rape, slavery, and even murder. While he didn't think any real magic was involved, that didn't make it any less dangerous. He vowed to stamp out any signs of it should it ever crop up in the Vale.
But it was because of this, and the Faith's highly negative views on magic, that made Jasper decide to bring new life to the Old Gods and try to encourage their worship. He knew that eventually his magic would be revealed, and followers of the Old Gods were far more accepting of magical abilities than the Faith. He disregarded the followers the Red God entirely, as that seemed little more than a dark magic cult. Thankfully, it's presence didn't seem to yet reach the Vale, although it was gaining a lot of traction in the Targaryen court. He hoped that the more the Old Gods and their actions seemed to spread throughout the Vale, the less of a hold the Faith and these other religions would have there.
By the time Jasper had finished his work on the Eyrie, another fortnight passed, and it seemed that the war was finally upon them. King Aerys had brutally murdered both Rickard and Brandon Stark, along with Jon's nephew Elbert and two of his companions. When the king then demanded that Jon send him the heads of his two wards, Lord Baratheon and the newly declared Lord Stark, all three raised their banners in revolt.
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AN: So, I know in cannon the Children did the Breaking during the arrival of the First Men, well before the Age of Heroes (The war with the others). However, in my version, the two happened at roughly the same time. While the children were dealing with the First Men, they were also fighting a war against the Others. They ultimately stopped fighting the First Men and turned to them for help, with the alliance eventually winning them the war.
I'm not sure in cannon how long Lyanna had been betrothed to Robert, but in my version, it had been a long time. They just weren't going to be married until Robert finished his fostership with Jon in the Vale, which was soon approaching.
Jasper's analysis of how the smallfolk view the Old Gods is almost a direct quote from Chapter 8 of, "Hadrian Lannister Lion of the Rock" by Sage1988 (On ). It's a really good story and I highly recommend it and his other works.
Now, it wasn't asked, but I wanted to expand upon my reasoning for putting in the well and the hotsprings. With the Eyrie being located on an isolated mountain top, there wasn't any source of water for the castle. Water would have to be brought in and stored, along with grain and other food. Now, water can be pulled directly from the well, reducing the stress it caused having to transport it into the Eyrie, as well as make it easier for the castle staff. I don't believe they would have used a cistern (Reservoir to collect rainwater) as that's too unreliable for a castle that size and the temperatures would more than likely produce snow or hail rather than rain. Furthermore, this ensures water can be used more frequently and frivolously, such as for baths and for the godswood. The hotsprings themselves can also be used to encourage good hygiene, although primarily, it was a place for Jasper and others to relax. - Someone in the comments had made mention of tunnels already existing beneath the Eyrie, but I believe those would be underneath the castle itself, and not the godswood. So, these additions should still be possible, and if not, please suspend your disbelief.
Notes. For those that know one 'verse, but not the other:
 Enchantments are magic worked into an object so that it can take on specific properties.
 Wards are magic that is tied to a specific location. These are typically permanent or long-term and are most often created using runes.