there's some nice ones in Sawtooths above Fairfield nice with Corral's ones called sawtooth camp ground little used to there are several others.
Twin Lakes camp ground has horse pens. Open only in Summer. You can get on line to see when it opens.
Private land owners may be able to accommodate you in a case by case basis. Msg me, I have contacts up there who will allow equine camping.
Not aware of one, may be some private operations.
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