Basically, as the title says, furs and hides should be distinct. I am assuming that climate will be in eventually because why the fuck not, and climates mean gear suited to the climate. When you are trudging through calf deep snow, you want some warm as hell deer or bear, not some hairless pig.
Some examples of why there should be a distinction: The above warmth idea. Because a furry waterskin sounds ridiculous and nasty. A difference between leathery and furry upholstery. Because.