The list under "Game Information - Players - skinnable animals" is outdated, so, in the recent trend of making new resources and updating old ones, I figured I'd update this. If I missed anything let me know.
Badger
Bat
Bear, Black
Bear, Brown
Bear, Grizzly
Bear, Polar
Boar
Cockatrice
Cougar
Crag Cat
Deer
Falcon
Hill Hound
Jaguar
Leopard
Lion
Malar
Owl
Panther
Rat
Raven
Stirge
Tiger
White Stag
Winter Wolf
Wolf
Worg
Dire Bat
Dire Badger
Dire Boar
Dire Bear
Dire Bear, Ancient
Dire Bear, Legendary
Dire Rat
Dire Tiger
Dire Wolf