Ive had the same thing happen , we likely all have . Snow just makes it easier to read the sign. Im thinking its a little of both but smell is likely the killer . As was said they see wire all the time , everytime they cross under a fence ...might still be a touch of human scent there . I paint mine too and the air out before storing in sealable gallon cans with leaves and sage from the snaring are . Take the lid off and the sage scent is quite strong

Here we have human foot traffic often enough I don't think it bothers the coyote if you walk on trail, sometimes in snow I come it from side to hide tracks.
What Boone says, Brite nights see more refusals, the snare is always partially blended with 2-3 stalks of grass, unless the grass is already over hanging the trail.
I sometimes set wide open trails in shorter grass, put in a weed or two to block other openings, and a thin weed to hide support wire,
Never fails, dark night comes along and these open trail set connect, had one this year, big male

Rob has it right.
Walk through your sets.Do Not walk around,or make set and turn around and go back.

Newt,
What about snare sets going to bait piles in snow? Just curious.
Mac

This! I try to set my snares in the trail where there is a slight bend in the trail. The snare is not silhouetted against the trail then!