Apparently girlfriends stealing your jacket is a thing? M15 F14

I was confused about some random hoodie meme and my friend told me it's pretty common for girlfriends to steal your jacket. Something about boyfriend smell and warmth. Never heard of that before, but I think that sounds adorable and just the right amount of romantic. Would it be weird to just give mine to my gf? Like just as a random gift thing? It's my first real relationship, so I'm very inexperienced with this sort of thing. We've been dating for three months. Would that come across as possessive? I do intend to ask her first, of course. She's usually the more logical and pragmatic one, while I tend to lean towards the more emotional and admittedly naive. I feel like it's something she might like, but I'm not absolutely sure.
TL;DR!: Heard that gf stealing your jacket is common, thought that sounded really cute and romantic. Would it come across as possessive to just give mine to her as a random gift sort of thing? I'm going to ask her first ofc.


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