Horse Protection Amendments Act This bill amends the Horse Protection Act to replace the Designated Qualified Persons program responsible for inspecting horses for soring with a new inspection system. (The soring of horses is any of various actions taken on a horse's limb to produce a higher gait that may cause pain, distress, inflammation, or lameness.) The Department of Agriculture must establish a single Horse Industry Organization (HIO) in order to establish a formal affiliation with the management of each horse sale, horse exhibition, and horse sale or auction, appoint inspectors to conduct inspections, and otherwise ensure compliance with the Horse Protection Act. The Commissioners of Agriculture for Tennessee and Kentucky must appoint individuals to the HIO. Those individuals must appoint individuals representing the Tennessee Walking Horse industry.