I should say at the outset of this article that I am a vegetarian, and I generally think of animals as cute and fuzzy friends of the human race. I have no moral objection against hunting animals and using their bodies for food or clothing, however. Logically, it makes sense that people have needed this to survive, but emotionally speaking, I find skinning and eating animals rather distasteful. Things would have been different for me if I had been raised on a farm or in a hunting community instead of a city thoroughly saturated with the culture of Disney movies about cute animals singing songs and having adventures, but... anyways, you are what you are. Hunting enthusiasts should feel free to write their own articles on the topic if they have different points of view.
So, anyway, as my vegetarian brain started churning around this idea of how skinning can be roleplayed in World of Warcraft, I couldn't help but admit to myself that I don't have so much real life experience of the topic. In fact, my first google search of "Skinning" turned up none other than WoWwiki's page on skinning in WoW, and I realized most people living in cities probably haven't got the first clue of what skinning animals is really like.
So I searched again for "skinning animals," and this time I found various articles about how to skin an animal for people who are interested in surviving in the wilderness, or just into hunting in general. One site even had simple hand-drawn animations of the proper way to kill and skin a rabbit, and I was struck by how very different this was from my experience of skinning in WoW. In the animation, we see the head and feet get cut off, a slice go down the middle of the animal's body, and the skin slowly peeling away to reveal all the flesh underneath... while in WoW we just right-click on a dead animal, loot its hide, and poof -- it disappears before our eyes.
Now, normally I say that what you see in WoW is what you get. If there are mineral ores sticking up out of the ground in grassy plain in the game, then Azeroth is a world in which mineral ores stick up out of the ground in grassy plains. As roleplayers we just adjust to that, we find reasons for it, and our characters play it out as if it's a totally normal thing.
Skinning, however, is an exception. Here, it seems clear that the omission of actual blood and gore from this profession is more of a nod to parents of children who may be playing the game than it is an actual declaration that blood and gore do not exist under the skins of Azerothian beasts. To a certain extent, this blood and gore is represented when you can click on animals and loot their various meats, but that's obviously a different feeling from real life skinning.
So the challenge for a roleplayer is to understand what skinning really is, then turn around and let your character act as if this blood and flesh is what he's seeing every time he skins an animal. If your character is someone like me, who thinks animals are cute and friendly, who would see a pig and think of Babe -- not dinner -- then skinning is not the profession for you. Your character has to be comfortable getting his or her hands bloody and taking bodies apart.
Skinning with class
Hunters are obvious choices for skinners, of course -- they just go together like peas and carrots! In a way, it's odd that some hunters might not be skinners. Why wouldn't a hunter skin any animals he kills? If you play a hunter who is not a skinner, it would be a good idea to think of a reason why. Maybe your non-skinning hunter is more of a sharpshooter, or an animal trainer, than an actual wilderness survivalist, or maybe he's just a vegetarian.
Other classes who generally hack their enemies to pieces wouldn't necessarily know how to skin animals, but they wouldn't be averse to it either. A warrior, rogue, or especially a death knight who has a problem with the sight of blood and flesh would be strange indeed (and interesting, if you could make it work)! Feral druids, enhancement shamans and retribution paladins would likely feel similarly. A character of these classes who is averse to the actual sight of blood is not beyond the scope of the imagination, but would require a bit of ingenuity.
"Softer" characters, who focus more on magical abilities, healing, and other sorts of activities without much blood and dissection may find skinning animals repulsive. Priests and mages in particular may be quite unused to the sight of it, though of course there could be any number of reasons why a priest or mage would have no problem with skinning. One just has to give it a bit of thought. Perhaps your priest is like a medical student who just can't get enough of dissection and anatomy. An more macabre skinner priest (especially an undead one) might even extend this interest beyond skinning animals, to include dissecting dead humans as well -- purely for the sake of knowledge, or so they say. A skinning mage (especially a troll) could go even farther, into complete madness, by writing his scrolls and spellbooks on the skins he takes from dead animals (and... people?) because he thinks it gives his spells extra potency.
Warlocks might relish the sight of animal blood and flesh being torn apart. After all, could a class who specializes in curses that rot away living flesh and explode all the blood vessels in one's eyeballs possibly have any problem with a bit of skin coming off animals? It would probably give them ideas for new sorts of curses they could cast.
Me hates dem aminals!
Another obvious possibility for a skinner of any class is that he is simply mad with animal-hatred. As Fargostar5000 pointed out in a comment on a previous article, your skinner could be "an anti-DEHTA crazed poacher," or even "some kind of squirell vanquisher." Does your character think that the Druids for the Ethical and Humane Treatment of Animals are a bunch of flower-brains? Does he kill animals, take one small part (such as a tusk, or toenail) and then leave the rest to rot, merely out of spite? If so, then skinning is the profession you could use to express that. Or perhaps your character has a crazy mad phobia of things that lurk inside the body of furry woodland creatures, and must take animal bodies apart in order to be sure that wicked demon creatures will not burst out of their corpses.
In short, skinning is yet another profession where your character can go nuts and be very creative, albeit this time in a rather unsavory fashion -- yet at the same time, skinning is a good choice for the simple, down-to-earth character who just wants to get by in the wilderness, and use all of nature's resources in a responsible manner.