The term 'Parts of Horses' Harnesses' can be broken down into two seven-letter crossword solutions: 'BRIDLES' and 'REINS'. BRIDLES are pieces of equipment used to control a horse, consisting of a headstall, bit, and REINS. REINS are straps attached to the bridle that are used to guide and direct the horse. Both BRIDLES and REINS are essential components of a horse's harness, which is used to attach the horse to a cart or other vehicle.