I've lived and worked in Virginia, both Carolinas (on the coastal plain) and central Florida. Spring can be nice, mid-March to mid-May, earlier the further south. The n it starts heating up (humidity is always there. Gets nice again late September well into November, except Florida, which stays warm longer depending on how far inland, how far south.
DC in the spring is special, for festivals, and for many of those early visitors being school trips. I find it the better time to tour, better people to tour with (compared to families and adults stressed by crowds and heat).
I've been lucky on winter trips too, great weather from Monticello to Williamsburg, then Outer Banks and Grand Strand, between Christmas and second week of January. But coming from California, there is a great risk of having to deal with 1000-2000 miles of hard winter weather getting across the country to the coast.
Eastern mountain areas, even the Piedmont, is not the same as the coast. Coastal weather is moderated, maybe dominated, by the Atlantic, coast can be frost free most winters up into Maryland. Get away from the coast, winter weather down into Georgia, even occasional frost in northern Florida towards middle of the state.