Another American history fairy tale.
Napoleon was already soundly defeated by the time winter hit. They were actually in full retreat when winter started. The vast majority of Napoleon's losses were during the summer when soggy ground conditions hampered their movement.
The same conditions defeated the Germans. Hitler thought they would advance quickly through Germany and the autumn and summer conditions slowed them down so much that they weren't prepared for winter because they thought they would be in and out by then. Like the French, the Germans suffered their casualties during the summer months. Nazi generals wrote Russia off as a loss before winter even started and knew they didn't have the supplies to hold off the Russians even if winter wasn't coming.
It's sad how the American education system failed us so badly. So much of what we were taught was more fairy tale than actual history.
Its how you control the populace.