I'm doubting he would use the skin for warmth. Hell of a lot of work for a minimum result. Assuming for whatever reason he can't do a fire again, I'd look for small caves, crevasses in rocks, low spots in the ground, a fallen tree, or other natural block for protection on one side. Then leaves or branches on the other side. If he's got the tools for skinning, he can create a reasonable shelter in a lot less time.
However, I could see him skinning the critter as a trophy. I'd see him spending some time doing it as right as possible, which if he has a knife, water, fire (to create ash), and some time to work the hide, he can do a reasonable job of the process.
Best of luck,
Jim Clark-Dawe