Snow is not a problem for trailers, water is. I used my trailers 12 months out of the year and if it meant that I had to shovel out the snow, that was fine. The small amount that is left behind was never a problem.
BTW, on my trailers, I used plexiglas on the open areas of my trailer to cut down on the wind when I hauled in the winter. On one trailer I installed rails to slide the plexiglas in or out.