No reason to not bring horses. Keep in mind that there are no "campsites" rather a large area that RV's park in with zero services.

Are they allowed, yes, it's National Forest land and there is no stock animal ban. Would I tow a trailer with horses up that road...absolutely not. Keep in mind there are (large) predators in the area and there are no services set up for horses like available water sources, paddocks, tie outs, etc.