It's become very rare now, but this happened three times in the 80s (82, 83, 86).
April 1982 everyone who was alive then remembers, but we also had 1 inch of snow a week after that.
April 1983 on the 19-20th we had 1-2 inches of snow
April 1986 a T of snow on the 23rd
Nothing in the 90s after April 10 (4/10/96 was the latest 4" at JFK)
2000s-- nothing after April 10th (April 7, 2003 4-8 inches, April 4, 2006 1 inch JFK).
2010s April 16, 2014 (1 inch), April 2 2018 (4-6 inches).
2020 Trace on May 9, 2020
So very few amounts of even a T after April 10th.