I first got my hands on the book about 12-15 years ago at a local library and haven't had luck finding it since. Sadly I don't know the name of the book or the author and all I have to go off of is the cover image and the very few details I remember, though I was in early middle school at the time and the book was above my reading level.
In the beginning of the book it was following a female character who was in hiding during a war. She had to keep her hair dyed dark to hide her heritage, this included all hair on her body, not just on her head. The cover image was a man in a gas mask riding on a dragon while the background looked like an active war zone.