He amused himself for a moment, picturing Dumbledore, with his long silver beard, full length wizard's robes, and pointed hat, stretched out on a beach somewhere, rubbing suntan lotion onto his long crooked nose.
There was a whisper, also, about securing the gun, and keeping the old fellow from doing mischief, at the very suggestion of which the self-important man in the cocked hat retired with some precipitation.
Traditionally, wizards are old men with long, white beards; the traditional dress is that they have a very tall hat that comes to a single point, what we would call a pointed hat.