I believe there is some sort of correlation between the fall-months and winter months, however, I think the biggest issue is correlations are trying to be tied into specific variables (temperature anomalies, precipitation anomalies) as opposed to pattern structures and evolution. We all get excited when we see specific pattern regimes which have a strong correlation to producing weather events, however, I think sometimes the excited gets too overstated. Re-analysis is extremely helpful in that you can find 10-big events and come up with a pattern correlation, but I think the one thing we are lacking quite a bit in is with "misses". The KU books get into these which is fantastic, but I think outside of this book there really isn't a focus on these.
You could get a pattern which produced 2 big storms before and we know this because we have the events to do reanalysis on, but how many times has that pattern regime occurred with nothing happening? Perhaps something exists out there but I wish there was a way to measure the # of storms per winter...now you would have to come up with some definitions and set parameters but something like this, IMO could add tremendous value to long-range forecasting and even medium-range forecasting.