In theory, since the sprockets are so wide, and the belt lacks holes, snow/mud that gets between sprocket and belt will be packed into the notches and could build up if conditions are right. This could build up to where it locks the belt (or damages it, if the rider tries to force the thing), in the worst case. In any case, it's not going to make pedaling any easier.
I was just reading where truck off-roaders have a lot of trouble with mud in their serpentine belts, in some cases damaging the belt or the bearings of the generator or idler.
No experience with bicycle belt drive, though, in any conditions.
I do notice, in the belt tension thread, that the front sprocket has large holes in it and, one would expect, would not have much trouble with snow/mud buildup. The rear sprocket (in the image presented) is not seen well enough to say if it has holes in it, but it looks like not -- at least not as big as the front. Other bikes may be different, of course.