This question addresses a tricky situation. The horses in question are at a ranch that allows the public to go on trail rides. So there is more to consider than just getting the horses to go forward…maybe it isn’t going to be best for safety reasons. But we can always add positive reinforcement into their lives to help them to enjoy their time with people, even unskilled riders. It might even be a great way to help people learn more about equine behavior and to use something besides pressure/aversive when interacting with horses. If you decide to teach them to go forward, I would suggest also reinforcing the cue for downward transitions so that you don’t lose this valuable safety tool.
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Also, check out: wwwconnectiontraining.com. Connection Training is a community for discovering about and applying positive reinforcement training. It is a safe place to learn and share as you go.