Speaking of late snow, May 25, 2013 (Saturday of Memorial Day weekend) was darned close and I suspect parts of the area did have snowflakes mixed in. The high temp at ISP that day was 49 with about 3/4" rain and strong NE winds. I took my son to a track meet at Randalls Island and it was a miserable day (but we did get to see Usain Bolt in his prime). It was windy, rainy and cold and at one point I thought I might be seeing some white rain in the mix. Maybe I imagined it. Meanwhile, upstate this was going on:
https://www.mynbc5.com/article/whiteface-mountain-gets-three-feet-of-snow/3309477
The Catskills got snow that day too. I think something similar might have happend around Memorial Day 1967.