There are wooded paths that are open to trail riders but they are at least a 60 min drive (not horrible), but not as simple as hoping on your horse and heading out directly to the woods. For those reasons trail riding isn't that popular in my area. It's not always a question of whether you want, but is it even accessible?
The access to trail is probably one of the biggest things preventing people who want to take their horses on trail, from being able to do so. Some of it is due to closure of land that used to be open to riders, or sometimes it's just lack of parks that offer enough trail distance to make it worth the drive.
For me, if it's under ten miles, it's not really worth hauling an hour just to get there and ride for the day. Only possible exception might be the 8 mile loop trail at Liberty, IN - just because it's VERY well maintained, perfect for our gaited horses, and we get there early enough to ride it twice. We do one loop, go back to the trailer and eat lunch while the horses take a break, then hop back on and ride it in reverse. Not exactly a technically challenging ride, but good for getting horses in shape. Plus, you get to ride alongside the main public campground area for a hundred yards or so; dogs, fire pits, tents, awnings, kids on bikes, and a whole bunch of other spook-worthy things.
Along the same lines as the OP - even among trail riders there are differences in what kind
of trail people prefer. Personally, I like some challenges along the way. . .but some of the trails I like, other trail riders might call a "goat path" or "mule path" because it's narrow, with lots of roots and boulders and steep hills and places that require the horse to think about where it's putting its feet. Moving along on my little gaited horse is fun, but I start to get bored if it's nothing but flat wide-open trail - but for other people, that's as much "adventure" as they want, and that's fine, too.