I had taken their water away and was only giving them water from little one gallon waterers (frequently filled). Honestly I have NO IDEA how he managed to get that much ice on him from the little trough around the waterer. There wasn't even that much spillage around them. It's a mystery. We haven't had much snow either. It reminded me of tundra for a few days there. Dusting of snow but otherwise a barren, windswept landscape.
I'm in Michigan, it hasn't been quite as cold as you've had it (got down to -3 a night a few nights and a high of 8 one day there - wicked windchills, though) but still cold. I tried to catch him and stick him in a dog crate to bring him in and let him thaw. All that did was show me that I need a better net for the scovies. It's OK for the turkeys but the smaller (which is relative - he's a BIG duck) bird just got tangled in there and by the time I freed him from the net I didn't have a good enough grip to hold him. Once he got away once I couldn't get near him with the net again.
I did add scads of extra straw to the coop though. I'd still like to know how he iced himself up like that...