I'm glad you asked that question, Michelle! I've been wondering the same thing. Like you, we don't use any kind of heating either, but rather choose to rug up as warm as possible. I do blow-dry the Beaks and they love it probably more than they enjoy their mist-baths. Don't be afraid to try it with Percy: it won't hurt him, so long as you keep the blast a fair distance away from him and only use the 'warm' setting. The Beaks love being blasted with the fan set on 'high' and they fight and jostle each other to get right in the path of the warm air. It's a great way to dry them after a thorough wetting and they'll spend a good half-hour preening, then sleep for ages.
But, as you say, is it OK to wet a bird to the skin in the midst of winter??? Especially a bird of tropical origins???
Additional: You could make a sort of bottomless box arrangement for Percy to roost in of a night. I just made some hanging curtains out of a piece of old fleece for my lot to roost in. Needless to say, you'd think I'd just introduced Godzilla to the cages, but I'm going to leave my arty-pharty curtains for at least a week. I'm especially worried about Dommie, who is naked on his back and on his front. If it gets really cold, I'll have to figure out some way of bringing him inside again. You'll hear my husband hollering if it comes to that! LOL! I'll let you know how the curtains pan out. If they pan out. LOL!