There are definite dress codes where I work i.e. no visible tattoos, one small earring in each ear, modest attire, etc. (For the most part, though, they are unenforced.)
I always wear my hair down. I guess to some it could look a tad unruly. But I wear the sides up. This makes me feel more groomed and I don't have to mess with it falling in my face.
No one has ever mentioned that I should do something about my hair.