Not downplaying any of your points about climate change but wondering if the difference had more to do with measurement technique than what was actually falling from the sky? NYC back in the late 1800's to 1930's would have been about as cold as the parts of the mid hudson valley today. These areas are averaging over 40" per year currently and they are further from the coast so maybe are a bit drier, while NYC back then was still around/below 30" per year if Im not mistaken?
Were the people doing the measurments back then including every storm no matter how minor? Were they measuring every 6 hrs during large storms or just plopping in a yard stick at some point after the storm was over with compaction already having taken a serious bite out of the totals?
Seems data integrity could at least be part of the story.