In 1941-42 the first snow was anywhere from the last week of September to the last week of October, depending on how far north you were. In 1812-13 the first snow was roughly a week later. The main differrence was the temperature; in 1812-13 it never got much below -23 Centigrade (-10 F), where in 1941-42 it got down to -35 Centigrade (-30 F).
With colder temperatures both sides suffer even more than OTL, which would preclude any sort of organized retreat or pursuit. OTL out of roughly 600,000 French and French allies and 400,000 Russians at the start of the campaign a mere 25,000 French and 40,000 Russians were still with the colors at the end; one could argue that Marshal Winter was the only victor. If it's colder and snows more mere handfuls will survive.