The outer covering of the body

As a cold day unfolds, two enemies meet and pull each other's hair out. 
They pill layers off of each other, as if they were a couple of onions. 
Skin, so says biology, is the outer covering of the body. 
And so it goes, that the enemies find themselves most reviled in front of each other. 

Inspired by the words: cold, hair, enemy, unfold, biology, ski, onion. (and a Wikipedia definition for skin).