Photoperiod drives the moult. Shortening autumn days initiate the change to a white winter coat and lengthening spring days reverse it, on a schedule that evolved to match the historical snow season at each latitude. The trigger is largely fixed within a population, so the hare cannot simply wait for snow.
As snow cover has shortened at both ends of winter, field studies in Montana and elsewhere have documented white hares sitting on snow-free ground. Researchers have measured elevated weekly mortality for mismatched animals, since a white hare against brown litter is far easier for lynx, coyotes and raptors to detect, and the hares show little evidence of behavioural compensation such as choosing matching backgrounds.
There is a source of hope in the variation itself. Some populations carry genetic variants for winter-brown coats, in snowshoe hares apparently introgressed from black-tailed jackrabbits, and moult timing varies between individuals. Whether selection can act fast enough on that variation to keep pace with the rate of snow-season change is the open question.