I haven't had any problems (footnote -- during MOST of our WDW trips it's off season & I don't want to walk around with wet-hair AND during most of these trips my hair was halfway down my back and VERY thick [I have to have it thinned on a regular basis], my braid was about 2" wide).
The blow dryers have consistently seemed powerful enough to me (the only one I ever had a problem with was at Boardwalk Inn & that one sounded like it wanted to blow up not blow dry).
EG