It's funny how you can share dreams with somebody but not learn their odd quirks until later.
Like how Ariadne wears socks to bed, but always kicks them off in the middle of the night. Or how Arthur makes coffee once he wakes up, but he doesn't drink it, he just smells it- Ariadne's partially glad, because she doesn't want to find out what he's like on caffeine. She bets that he would be a force to reckon with.
Arthur secretly adores the feel of her bare feet against his legs in the morning- but he'd never tell her that, because she might change. And he loves her scarves (he really loves the way they feel in his hands when he's pulling them off of her). And Ariadne's glad for the scent of coffee that goes untasted, because it reminds her of him and their home. And she likes how his bookshelf is organized- alphabetical order by title, so everything's easy to find.
But what they really love is the way they fit each other to a tee. Not only physically, but in every way possible. She designed their loft (of course she did, she's an architect, that's what she does), but his touches just made it complete. And how he just knows that she likes her water glass with exactly three cubes of ice- it's an odd habit, but it just seems to fit her and he loves it.
He loves everything about her.
So of course he goes and buys a ring. And because she loves everything about him, she says yes.
But, being the nontraditional dreamers they are, Ariadne doesn't wear the ring on her finger during the day. She weaves it into her scarves, diamond against her neck (she's still practical, and there could be people looking for them). And he insists that she can wear it on her finger, she'll be safe, because he's there to protect her. She just smiles and promises him something for later.
And yes, she'll be wearing the ring on her finger, and not in her scarf, then.