Coyotes can often be fooled with a hay set. When it gets too frozen to dig a trap bed, switch to hay sets. Just pick up a few armloads of hay, and throw it in the back of the truck for your sets. Another reason to use a hay set is the eye appeal. In hay fields and open fields hay is a natural thing. It stands out, but is not unnatural. I also use hay sets if there is a lot of mud around. You don’t even have to dig a trap bed, lay the trap on a fluff of hay, cover with more hay, add lure and/or bait, and the set is complete.
Once you catch a coyote in the hay set, you will need to know how to remake the set. This is a good video to watch.