The only real changes I see in the country I typically hunt, is related to resource availability. Which, depending on how severe the winter is and what resources there are to begin with, often doesn't really change at all with the temperature.
The coyote are usually in pretty much the exact same places as they were when the days were warmer. With maybe some difference in layup locations - like sunning themselves rather than laying in the shade, but, the difference is only 50 yards in position. I'm only interested in which ridge or draw they are using, whether they are a couple hundred yards one way or the other rarely makes me any difference.
Most of the time. Most of the places I hunt. Which is high desert, no agriculture - no fields or irrigation or crop or any of that. Maybe a pasture bottom or alfalfa field here and there, in some places, but that's about as close to "farm land" as I ever get.
Some years, some places, deep snow or really unusually cold temps can rearrange resources - things like winter killed cattle, road killed deer, yarded up jack rabbits etc., will have obvious effect on the habits of the coyote in the immediate vicinity - and sometimes the "immediate vicinity" can be pretty large. This kind of situation is as plain as the nose on ones face though, doesn't need explaining.
For the most part though, all the cold weather really means where I hunt, is that it is getting later in the season and all the easy/dumb ones are already dead or wised up, coyotes are starting to pair up and think about mating, and calling just generally gets pretty slow, compared to the warmer days of fall.
- DAA