I've been watching a lot of the MCU while in quarantine. It hit me that when they show Steve frozen he is laying down. That means that at some point he was conscious enough to move from the front of the ship to his laying down position. So here's 300ish words on what might have been going through his mind.
Steve unhooked the harness holding him to the pilot's chair with a shaky hand. Cold started to leak in to the hull almost immediately. He allowed himself just a few moments of self-pity. He would never get to dance with Peggy, he wouldn't be around to celebrate the end of the war, his life was ending. Truthfully, with all his ailments, he always assumed he wouldn't live a very long life. But then the formula gave hime renewed hope; the potential of a long life.
It was ok though. He wasn't going to get to live, but that was ok. Peggy would be fine, she'd move on and probably do some amazing things. The Howling Commandos? They would be fine too. He saved the world, so it was ok. The cold started to seep into his bones, reminding him of many winters spent in poorly heated tenements. His limbs started to feel heavy and his brain started to turn to much. He needed to lay down, so he did. He kept the shield over him, maybe it would keep his core warm just a bit longer. There were no thoughts of escape, this was the end.
He wouldn't get to be buried by his parents. That made him sad. He wasn't really leaving anyone behind, no family, just Peggy and the Commandos, and Stark. They would put together a nice memorial for him, so that was ok.
He was starting to feel tired. He lost the monumental battle to keep his eyes open. He was freezing now. It was ok, though, right? This is how Bucky had gone out, alone, in the cold. If it was good enough a death for Bucky, it was good enough for Steve. This was the end of the line.
He just wished he had a chance to say goodbye.