Her appearance as far as I can tell is just an artistic choice. If you go back and look at new New 52 Batwoman, she looks relatively normal.
Example of Pre New 52 The pasty white look also begins to lessen in intensity over time. Not sure if this is just an artistic choice too.
And the long red hair is in fact a wig. It's simply a way to help hide her identity. Theoretically yes, long hair would make it easier for badguys to use against her, but like most long haired super heroes, this just gets glossed over for the most part.