Hunted them in about a foot of snow and very low temps in the Black Hills one year. It was tough hunting, they would gobble on the roost but not much on the ground. Easy to spot in the snow, easy to track, but mostly looking for food not love. Didn't have much luck calling them in and I didn't get one that year.
When KS archery used to open on the first of April, I spent some pretty cold days in the woods. The photo in my profile pic was from the first of April, no snow on the ground, but it was 20 degrees... I about froze to death, but one of my favorite turkey hunts ever. The birds gobbled like crazy, and we had over 100 in the field in front of us.
I've always hunted turkeys like I hunt deer. Hunt food sources, and use decoys and calling secondarily. Unless there's too much snow for the ag fields you have access to. Pop up a blind, light your buddy heater, and pack a lunch. The kid will tell you when he's ready to go home. Good luck
