Well, 19 samples is too small to make definitive judgements, but anecdotally, it sometimes seems like what you might call weather "regimes" or "patterns of patterns" seem to have a wavelength of 1 to 3 months. So for you guys, late January and February seem to be your snow moneymakers, so if you are having a March which is in any way conducive to snow, then perhaps that means that there is a better than average chance that late Jan and Feb were warm.
Conversely, when you have a good Jan and Feb, it may be more likely that March will be warm
Or it could just be random chance.