Not all areas are the same. I live in far western Wyoming. High elevation. Mountain ranges all around, which pretty much function as snow magnets. Three feet of snow or more on the ground is not unusual in the winter here on the west side of the continental divide. So that's why Jackson Hole is such a popular ski resort. We get a ton of snow. It's a challenge to move all that snow to clear roads and driveways, but it's doable. It's worth it. We snowmobile, so that helps.
A clear night in the winter is usually cold. I think it got down to 38 below zero this past winter. Hasn't been below -20something in quite a few years. But it happens. My wife grew up here and she remembers one cold snap back in the 80's when it was -58. Power lines start snapping at that point. She said it really sucked. But that's not a frequent occurrence at all.
On the east side of the continental divide, you're looking at not much snow at all during the winter. But when March or April rolls around, you'll get a couple of snow storms that dump 12-18 inches of snow. That would include the major metropolitan areas of Cheyenne and Casper. Yes, they are around 50,000 population each.
If you're entertaining the idea of relocating, I'd suggest a 7-10 day tour of the state. It's a large area. Even if you don't make the move, you won't regret it if you're into the beauty of nature in a very rural setting.