Complex sentence: Most horse shows offer Halter classes, also called "breeding" or "In-hand" classes, where the horse is led, not ridden, and its conformation and gaits are judged.
Split into simpler sentences: Most horse shows offer Halter classes, also called "breeding," "conformation," or "In-hand" classes. In these classes the horse is led without a saddle, not ridden, and its conformation and gaits are judged.