I dont know how belts on snowmobile works but assuming there isnt a lot of literal slipping happening, I would imagine a pattern, because the spots are not all over and are in those spots, are from defect or an alignment of assemblies or a crankshaft or other pulley runout, and the wear is from the same spot hitting a variation over and over
What kind of cold are we talking for freezing the belt? Haven't heard of anyone who's blown a belt because it froze up, so I suspect it applies to other parts of the world than where I live
