While there are no hair dryers in the albergues, lots of female pilgrims have long hair, so there's no need to cut it short. it's simply a matter of washing the hair and letting it dry naturally - every woman will be doing the same thing. When walking wear it however you prefer, in a pony tail, hanging loose, it doesn't matter. The Camino is not a fashion parade, and no-one will judge you by the way you look.
However, I have to admit to the occasional night in an hotel to take advantage of a shower and room to myself, plus a hairdryer!