Near Flintstone, the 40,000 acre Green Ridge State Forest has miles of trails and forest roads open to horseback riding. This region is very dry, so the riding is almost year-round (so dry that theres even prickly pear cactus!).
There is also the nearby 18 mile C&O towpath trail.
Overall, Green Ridge State Forest is the 7th most popular horse trail of all 10 horseback rides in Maryland.