They won't dry off since its freezing, it will become ice clothes instead.
Sorry fir double toast but I'm too lazy to edit my last one.
Taking that into consideration, you find a large snowdrift, make a shelter of some sort (if you dig in it'll be fine) and seal most of the mouth off. The snow will insulate the area and keep you warm(er).
You might want some sort of small fire or light source and something that can keep you warm.
Option A: Make fire, warm clothes.
Option B: Wring out clothes. It won't be completely dry, but drier that what you had.
Option C: Option B then go out, look for dry wood, Option A (outside, otherwise you'll suffocate)