Since record keeping began at DCA (I believe in 1941?) April 13th of 1957 is the latest date for measurable snow there when 0.1" accumulated.
However before then, when snowfall was still actually recorded within DC, April 28th of 1898 saw 0.5" of snow (the latest measurable snow in recorded history).
Now still before that, in the pre-record era, accumulating snow fell from Northern Virginia through the NE corridor on May 4, 1774 with 4 inches falling in Northern VA and even more falling in places northeast. This was recorded in diaries.
However the latest date that DC has ever seen at least a trace of non-measurable snow was on May 10th of 1906.