Horses are allowed in Bandlands National Park [1], although there are no commercial horse-rental facilities. If you are bringing your horses with you on your trip to the hills, prime horseback riding country can be found in the Sage Creek Wilderness.
The Sage Creek Campground [2] has a section designated for horse use and a watering hole is located about a half-mile southwest of the campground. This is an easy place to park trailers and ride into the Badlands.
Horses are not allowed on marked trails, roads, and highways in the park but are otherwise allowed. Horse trailers can be parked at any overlook for day use but are not allowed to remain at overlooks and parking lots overnight.
Links:
[1] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-badlands/badlands-national-park
[2] http://www.moon.com/destinations/mt-rushmore-the-black-hills/the-badlands/badlands-national-park/accommodations-and-food