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difficult to answer all those questions as they're overly broad in scope, but the more time you spend in the woods noticing these types of things the better your understanding of animal movement and behavior will be. It could be that the coyotes were moving down the trails and roads during the storm and their tracks were covered, it could be that the mt lion was moving to a new area or working that area for a while longer.
Or depending on how much snow you got the coyotes stayed in the woods more as there’s less snow under the trees. Or if there’s a crust on top they’re light enough to walk on top. But when the snows deep they’ll prefer the path of least resistance, run some snowmobile tracks around then come the next day and I almost always find coyote tracks on the snowmobile trail.