Unless i'm extremely unlucky, it seems it only works when skinning large game on the floor, but not game that can go into your inventory (i.e squirrels, hedgehogs, rabbits, etc).
Seems strange that I can pull 4 fox's worth of hide off one fox, but i'll never be able to get 2 rabbit hides off one rabbit.
Related: Letting hunter's extra meat work on small game too. Particularly much more useful with animals that only give one or two pieces of meat.