Towing a trailer off of paved roads is when ground clearance becomes really important - of both the trailer and the truck.
The 4Runner TRD has close to 10 inches of ground clearance, so you are pretty good with the truck. Ground clearance of your 2007 Chevy 2500 may actually be lower than the 4Runner, depending on how the 2500 is configured.
Maverick and almost no other trailer makers list ground clearance of their trailers, but in general trailer floors are at about 10 inches, and the axle tubes are lower. Measuring my two bumper pull trailers, floors are about 10 inches, axle tubes are 8 inches, and the leaf spring mounts are under 6 inches above the ground.
Then there is the hitch itself. The ball is going to be about a foot above the ground, but under that is the tongue to frame structure which is only about 6 inches above ground level. So as your rig becomes a “V” as the truck goes uphill with the trailer still going downhill that may dig into the ground.
So, IMO, the best for off-road horse hauling would be to keep your Chevy truck, and shelve the bumper pull-Toytota idea for a gooseneck trailer. The shorter the better, to make those tight turns. You could add bigger diameter tires and wheels on the trailer, or even have the trailer lifted. I have seen pictures of lifted horse trailers, but have never seen one in person.