It's probably a matter of just how packed and dense the frozen stuff is at heights more than a half foot as to whether or not you end up high centering on it (that, and just how much you are lowered, if at all), with the proper tires, of course.
The very fine powdery stuff you will be able to just plow through more than a foot, albeit visibility might be a problem when you throw up a big 'cow catcher on a train in many feet of snow' type of
forward rooster tail of the white stuff.