Singing cowboys on dancing horses are popular at horse shows, rodeos (and here, a circus) in Mexico. The horse spins, trots or canters in place, moves sideways, or rears as the rider sings a favorite to the crowd. Depending on the rider's skill, the dancing can be rather clunky or quite precise.
One I saw in Texcoco several years ago sung part of his song while standing on the rump of his horse, and another stanza while sitting on the horse, which had been made to lie down. In between he trotted in place, cantered sideways, and occasionally emphasized a line by asking the horse for a sort of capriole, which was done a bit awkwardly, but to enthusiastic response from the crowd.
The performer in this video, Raul Gasca, is a famous Mexican circus performer (handles tigers, too!) and does a well-honed routine with this horse. There is an article about the Gasca family here (in Spanish).