The red uniform that is used at the end of the movie is not original. The Spanish Riding school never used a red uniform. Disney found the original brown uniform too simple for a gala opening and introduced these uniforms.
In 1945 after the 328th Regiment, 26th Infantry Division captured the renowned Spanish Riding School of Vienna, Patton, an expert horseman himself, requested a performance of its white Lipizzaner stallions. So on August 21, 1945 a show was put on for General Patton, a host of American officers and troops. He described the in his diary that day, calling it "extremely interesting and magnificently performed."
George S. Patton spent a lifetime with horses. He played polo, fox-hunted, and competed in mounted steeplechases. He was a participant in the first modern pentathlon at the 1912 Olympics in Stockholm, Sweden, placing sixth out of 23 in the equestrian phase.