If the horse is being judged, they are being judged on movement, manners and way of going, as well as suitability for the discipline. You want an relaxed, ground covering walk, a bright, forward trot and a balanced, slow, rythymic canter. Hunters are supposed to move with a sweeping gait and reaching stride with little break at the knee.
Wrong leads are marked down.
If the rider is being judged, you are being judged on position, control of the horse, correct diagnols and leads and overall partnership with the horse.