I've driven through Salt Fort State Park in Ohio and there were a lot of horses camped at the campground and people out riding the trails. This was before I had my horses though and we were looking at the regular campground for a possible motorcycle overnight trip. Looked like a nice place though.
Another nice park nearby there is Beaver Creek State Park. Again, this was before I had my horses and my husband and I rode our bikes there to go hiking. Lots of people riding the trails. Here's a picture I snapped while we were hiking. This was in late April 2007.
Another place to think about is further north in the Allegheny National Forest. We took a guided trail ride at Hickory Creek Ranch and there's another one nearby there called the Flying W I think. Both have overnight facilities for horses and camping.
These are all places I plan to go trail riding next year.