The problem with most 12v hair dryers is that they are pretty low wattage, at least compared to 120v ones. They will take much longer to dry, if they do at all.
is a review of one at Amazon. At 12 amps, this works out to 12 X 12 or 144 watts, or about 1/10th of a standard AC dryer. Still enough to kill your battery if used too long, but not enough to dry efficiently.
There are higher wattage 12v dryers available, however they require a high current connection; they will not work plugged into a standard 12v receptacle, and will kill your battery faster.