IAD lists a Trace on May 26, 2002 . (seen at 2 different listings. Don't know if I believe it though)
They also list Traces of snow in June 2015 and 2016, but by the temps listed, I suspect that's from hail or semi-hail. Gotta wonder about some of these obs.
eta: Well, BWI lists a Trace on May 31, 2017. https://www.weather.gov/lwx/bwinme
eta: OK, since we've started this....DCA lists a Trace on May 16, 1988...