Two snowbelts, driven by two different lakes
Western and central New York sit downwind of Lake Erie and Lake Ontario. When cold air crosses open water, it picks up moisture and drops it inland as lake-effect snow. Erie is shallow and can freeze over during a sustained cold spell, which shuts its snow machine down; Lake Ontario is far deeper and usually stays open, so the Rochester and Tug Hill side of the state can keep producing bands much later in the season. That single difference is why Buffalo and Syracuse can have very different winters from one year to the next.