I think by now this horse has been beaten around long past its lifespan. The problem that arises here isn’t the “choice” of having another form of warmth, it’s just that to have a mechanic such as this ingame would also divert resources from other mechanics at what seems to be a trivial matter.
Rather than having this system where you could slit open an animal and crawl inside it I believe a better and more suitable alternative would be to implement lean-tos and other shelters such as tents. Not to mention I’d like to believe that fire plows and drills will make it into the game so carrying firestarting tools is redundant.