You will be able to see clearly if the head is bobbing or the croup is rising. Use a tripod to hold the camera steady. Once you set your focal distance, do not touch the zoom. Instead, pan the camera horizontally, keeping the same perspective on the horse. Always be perpendicular to the horse's plane of motion.
Good lighting is a necessity.
Autofocus cannot function well in low light. Position cones on the course where the horse will be trotted. Elevate the lens so that it is aimed at the height of the horse's elbow if you are shooting the whole horse. If you are just shooting the feet, to show how the horse lands or moves, lower the camera right down to the ground. Do not angle the camera.