Yeah this is part of my "evidence-based argument" that I have seen lacking. I've seen a few theories like "when we get a cold pattern in October, we often see regime shifts every 4-6 weeks which line up for a poor early winter"....well, some of these patterns weren't even that cold, more like cold shots in an otherwise normal/mild October (both 2020 and 2011 qualify).
But even if that wasn't the case, 2020 just blew that argument to pieces with a good December pattern for snow including our largest region-wide snowstorm since 2018 or maybe even 2015.
But you can test the regime change theory anyway....it would say that cold Octobers should correlate significantly to shitty winters. But they don't.