Sovia,
Fortunately, here in Texas snow is a rarity so I have not faced that issue. However, I think that the only possible issues with snow would be:
1) A build-up under where the door rests when closed The door will close down until the weight is taken off of the string, a build-up up snow at the bottom of the door would prevent it from closing completely and it would rest upon the snow. I image this could be remedied by adding a sloping cover similar to an awning over to door to deflect the snow.
or
2) inside the tracks he door rides on preventing the door from opening. This could definitely be problematic if a build-up of ice/snow got in the tracks and prevented the door from sliding freely. The opener uses a string to open the door and a knot on the string to stop it when fully open. I imagine it would not take much to snap this string and then it would not open until the string was repaired.
Hope this helps.