There is a Stranger quest that calls for 5 beaver skins. But other than the odd quest, there is the Hunting Challenges (which you start by skinning a coyote). Other than that, you need to kill and skin 18 bears for an achieve. But its pretty much just for selling at this point. I becomes very profitable when you do grizzly's. I was at the A. Basin at night and I couldn't get back on a horse for all the grizzly bears charging me, got 15 in a span of about 6 minutes lol, thats including skinning time!
Not sure about skins but having some extra plants/flowers/herbs on hand when I started one stranger mission saved me about twenty minutes of searching for them, so I wouldn't think it'd be out of the realm of possibility to need skins for something similar. But it's probably too much trouble to worry about keeping them for something like that. Then again, if you're not in the need for cash (I know I'm not), then maybe holding onto them for as long as possible isn't such a bad idea.