Your description fits a "horse walker" not a "hot walker" (Hot walker is the person who cools the animal down following races, exertion, etc.). See:
http://www.patentstorm.us/patents/3981274/description.html (there is a diagram here). If you had a picture, that would be useful.
Horse walkers are commonly used at race tracks for exercising horses and for leading them during their training. A usual horse walker has four booms radiating outwardly from a vertically disposed hub. The booms are fixed horizontally, and the hub for rotating the booms is rotated by an electric motor through a transmission. Transmissions that have been used include either worm gears or gear systems similar to those used in automobiles. As the booms are rotated, one or more horses are led byhalter straps that are connected to the distal ends of the booms.
HTH!