What I do (here in MT the snow comes and stays till spring)
is clear out the snow to the bare ground and make my normal dirt hole sets . I line the trap bed with butchers paper(its waxed on one side) to keep moister from seeping up from the soil and freezing my traps. I use dry dirt that I bring to the set from home. make your set and try to smooth out your foot prints. Out here the temps dont go above freezing and even a light dusting of snow on my sets will not affect them.I carry a small dust brush with me to clear snow off the set when it snows on them. Hay sets would also be a good set, just put some hay under your traps to keep them from freezing to the ice under neath.