My wife and I own horses and she gives riding lessons to kids. Most if not all states have an equine law similar to this one below:
Except as provided by Section 87.004, any person, including an equine activity sponsor or an equine professional, is not liable for property damage or damages arising from the personal injury or death of a participant if the property damage, injury, or death results from the dangers or conditions that are an inherent risk of equine activity, including:
(1) the propensity of an equine animal to behave in ways that may result in personal injury or death to a person on or around it;
(2) the unpredictability of an equine animal's reaction to sound, a sudden movement, or an unfamiliar object, person, or other animal;
(3) certain land conditions and hazards, including surface and subsurface conditions;
(4) a collision with another animal or an object; or
(5) the potential of a participant to act in a negligent manner that may contribute to injury to the participant or another, including failing to maintain control over the equine animal or not acting within the participant's ability.