I have coyote running deer trails that go across a fence line. They are crawling under but there are a few deer doing the same. So the only option is footholds. You winter snow trappers. How can I set the trail in the snow and keep the trap working plus not destroying the trail so the coyote will shy away. Thanks for your help.

Use a drag to keep them from ruining the set

I explain my process in this video that I used for years with as high of success rate per set as when I used snares pre-2005. I have other blind trail set videos on my channel that were made in the field, snow & bare ground.
https://youtu.be/nTnS03bB6fU?si=D1MdduoPC8mnCddO

Assuming you're staying frozen, dig a trap bed in the snow in the most likely spots you find, wax paper under the trap and over it, then put snow on top with a shovel or scoop (do NOT use your hands or disturb the snow too much or it sets up solid) you can also throw powdery snow up in the air and let it snow back down over your trap. Drags are best for this application, I just throw them off the side of the trail in the brush and kick some snow over the chain. Then I lightly dust everything off with a spruce branch as I leave, and let the trail return to natural use.

If you make a catch down in the tag alders and brush where the coyotes are sticking tight to trails as where I set, there is no way to keep them from tearing up the immediate area because a drag won’t allow them to get any distance away before getting hung up. What you do is just move your trail sets up and or down the same trail. You need to move far enough so that the sight of the disturbed area doesn’t pull the approaching coyote off the trail too soon. Because of this I used all short chains on my drags but using drags help with minimizing disturbance when setting.

Ok thanks everyone, will need to use a drag there is no pounding stakes in. I have watched your videos Seldom you are very helpful. Thanks for putting out good information.