Final answer:
Hearing is the most important sense horses use to respond to cues from a rider, as they are highly attuned to sounds and can interpret vocal commands quickly and effectively.
Step-by-step explanation:
The most important sense horses use to respond to cues from a rider is hearing. Horses are highly attuned to auditory signals and can pick up on nuances in tone and rhythm, which allows them to respond to their trainers or riders. In situations as described, where a rider's commands need to be interpreted quickly, a horse's hearing plays a crucial role in ensuring a timely and accurate response to the rider's cues.
For instance, when a horse detected the sound of pounding hoofs or the resounding gunshot, its reaction was likely influenced by its sharp sense of hearing. Riders oftentimes use vocal commands along with body language to direct horses, and these animals are well-equipped to hear and differentiate between specific sounds that signal them to halt, go, or adjust their speed.