On the World results, you are seeing that many of the youth have shown and placed with multiple horses in the same class, because those classes are single work classes - halter obstacle, obstacle driving, hunter and jumper. In these classes, an exhibitor, can show as many horses as they want to, whether that exhibitor is a youth in the youth classes, an amateur in the amateur classes, or a youth, amateur or pro in the open classes.
In other youth and amateur classes (driving and liberty), each exhibitor can only show one horse per class.
In open halter and driving classes, multiple horses may be shown that are owned by the same person, however, that person will have to have a different handler for each horse. Each trainer or youth/amateur exhibitor can show only one horse per class.
There are various high point awards exhibitors can compete for. The youth division has awards for youth with one horse and youth with multiple horses, but the amateur division has only the award for an amateur with one horse.