what makes horses so agile

The horses have evolved adapting for the run. The hooves are the most obvious adaptation. In the animal world, the smaller the number of fingers/toes, the better is the adaptation for running - and modern horses only have one finger/toe. The bones and ligaments of the feet offer great leverage, and the muscles (especially the hind limb ones) are very well developed. The lungs are big and not pressed by supplementary weight. You can see much of these adaptations to the big cats - except they have more fingers/toes and a more elastic vertebral column.