The thing about wild game is the chance that it may contain parasites or even rabies. My dad goes deer hunting several times a year, and I have never eaten a deer steak cooked less than medium.
I eat my beef steaks as bloody as I can get them, but never a wild game animal like deer, duck, pork, etc.
There's nothing wrong with feeding your dog the venison, but I would definitely cook any wild game first, just to be on the safe side.
@JOEL: I always cook the chicken that I give to my dog, just out of fear of salmonella and my own paranoia. As far as USDA beef goes, its raw all the way. But I would never eat or feed my animals any wild game meat raw...