It looks like late May 1883 was anomalously cold across much of the eastern US. I found this on an Ohio climate webpage about a late May snowstorm that hit Ohio in 1883:
“A heavy fall of snow occurred on the 21st in the north-western parts of the State. Snow is reported on that date from Dayton, Sidney, Lima, Upper Sandusky, Wauseon, Lebanon, Westerville and Columbus. The greatest depth was 15.5 inches at Lima. At Wauseon, the depth was 6.5 inches, at Sidney 7 inches, at Dayton 2 inches, and at Upper Sandusky 3 inches. At other stations the amount was small. Notwithstanding the depth of the snow and the great area covered by the storm, so far as has been ascertained no particular damage to vegetation resulted from it. One of our observes, Mr. G. A. Hyde, of Cleveland, who has kept a meteorological record for many years, reports that he has recorded but three snow-storms in May during the last 28 years. These were on May 1st, 1861, one-tenth of an inch, May 2nd, 1869, two-tenths of an inch, and May 1st, 1877, three-tenths of an inch.”
A couple of weather maps from that site as well:
So it looks like it was a case with a strong low pressure area moving through the mid-Atlantic producing pretty heavy snow, and strong cold air advection into the SE.
Source:
https://ohioclimate.wordpress.com/2015/05/22/late-may-snow-storms-of-1883-and-1894/