I check my two boys daily. Cold is okay. Wet and cold is bad. But you know that
I keep towels out in the barn to rub them down when they are wet (could be wet from riding or wet from doofus standing out in the snowfall) and use stiff brushes to "fluff up" the hairs. Then a nice blanket on while I feed them and I check on them in an hour. If dry, blanket comes off and they are fine. If still damp, I fluff them again and reblanket with a fresh one. Never had to go more than two blankets.
I also use the heat from my hands to carefully melt off the ice from their eyelashes.