The correct preposition is "off". When someone falls from a horse, they are experiencing a separation or detachment from its surface. The phrasal verb "fall off" precisely conveys this action of losing balance and moving away from a supporting surface or object. It emphasizes the physical separation. For instance, one might "fall off a bike" or "fall off a chair."
Option "from" is less idiomatic in this specific context, though it can indicate separation (e.g., "fall from a tree"). However, "fall off" is the more common and accurate expression for detaching from something one was previously on. Option "on" is incorrect as it implies remaining in contact with the horse, which contradicts the act of falling. Therefore, "off" is the most appropriate choice to describe the action of falling and separating from the horse.