Coyotes can be caught in the snow by a trapper who is willing to work difficult for them. I have a few favorite trap sets for coyotes in the dead of winter, including a trail set, a chaff/hay set, and a urine stake set.
At this time of year, a male coyote has two things on his mind: mating and eating. In the winter, food is meager, so coyotes will wander.