The main challenge here for cars to overcome is that many, like Google's, are heavily based on centimeter-accurate 3D mapping data. (I am not sure where Yandex's sit on this.)

So giant piles of snow often means that all of your reference points on your fancy 3D map of the road are now obscured by piles of snow, and you still have to be able to position the car well enough that you know when to look for stoplights, crosswalks, and the like.

Is it possible some kind of algorithm could be used to reveal the hidden detail beneath the snow?

It'd be incredibly complex. You'd not only need to factor in the height of the snow, but how snow plows are likely to push and pile up said snow. The edges of the roads after a snowfall are quite varied in landscape as plows unevenly shove piles of snow off the road.