Pfft, Bosmer-Snow Elf. Mine is a Dunmer-Snow Elf. With Dunmer you can get a very light colour. Thus Dravin was born from his Dunmer Mother and Snow Elf Father.
Anyway it is annoying you can't get a hair cut as a Vampire. Why not, your hair can't die, can it? Even if you are a dead Vampire that would not stop someone cutting your hair.
Going on a tangent here, but your hair is technically dead the moment it leaves your scalp. So your hair is dead, except the tiny part of it that is in your skin.
On topic though, it does seem stupid that the face changer says she cant do anything to you if you are a vampire, even a hair cut. I think it was something to do with a technical restriction, something to do with vampire faces changing when they used the face changer's services, no matter how small the change you make. So even if you changed your haircut, I think the face changer would make you look like you weren't a vampire or something. I'm not sure though.