Riding horses have the stats of a light warhorse, but are not trained for war. Therefore, they won’t fight for characters, characters can’t fight on them, and they are subject to the panic rules for beasts not trained for war (90% chance to flee in panic in cases of “raging fire, sudden movement, loud noises, or strange smells”¹⁾

Note that the a rider must be mounted for the horse to be able to attack in second and subsequent rounds of combat.²⁾

Warhorses only have a 10% chance to panic when presented with “raging fire, sudden movement, loud noises, or strange smells”, in contrast to the riding horse's 90% chance.³⁾