^^ Finally something within my purview: Being hugged by wings would not be like a warm blanket at all.
The only "alive" part of the wing is the front/top "arm", the rest is just feathers, which like hair, do not have body warmth. Now down can be pretty insulating, but wings are made from contour feathers (Pennae conturae), in particular flight feathers. Those are long, very light, and only flexible to some degree before they break/snap. The best haptic example would prolly be a curtain made from euro banknotes, lol.
They're also likely covered in preen oil, kinda like sebum (or talc-like dust for some water birds or parrots* which is more like dander). I imagine it'd have a distinct smell.
Now for the good news: wings are definitely an erogenous zone. There are string- or hair-feathers (Filoplumae) spread throughout the wing to sense feather position in flight, essentially they're to feathers what whiskers are to hair. Thought the erogenous stimulus is pressure from the back, so the left here is perfectly wholesome, the right is Rin being a tease.
(*I actually don't know if this applies to the HALO-assault parrots, a.k.a. falcons, shame on me. And yes, falcons are just murder-parrots.)