My part just finished a combat encounter, and one of the players pointed out that non-combat trained horses will flee in battle. Since two of the horses used were not combat-trained, how do the rules handle this? I can't find it in the PRS. Is there a mechanic for dealing with this?
The fact that your mount is not combat trained manifests by requiring you to make a "Control Mount in Battle" DC20 ride check as a move action. If you succeed, you get to use the rest of your actions. If you fail, you can do nothing else but hang on. This is under the Ride skill on page 104 of the core rules.
But what if the characters have dismounted and are in combat? Will the horses not run away from the battle if they are not combat trained?
The characters dismounted and just let the reigns drop ?
Do they have a hireling to hand the reigns to, or is one of the party a designated horse holder ?
Does the horse know the "Stay" trick ? If so, the character could make a DC10 "Handle Animal" check as a move action to tell it to "Stay".
If they just dropped the reigns upon dismounting but combat hasn't started yet, the horse may just look for a tasty bit of grass or a shady spot. If combat starts they might shy from it, keeping a bit of distance. If the horse itself is attacked by something it fears, it would likely flee to a place of safety (is the barn nearby ?) but it might fight something smaller than it like a dog, especially if it's the dominant stallion in the "herd".
If the horse has fled but you can still see/hear it, and it knows the "Come" trick, you can call it back.
See the "Handle Animal" skill section page 97. A typical riding animal knows "Come", "Heel", and "Stay".
As an aside I usually have a "dungeon donkey" if I am in need of a pack animal.
A dungeon donkey has been blinded and deafened and is far less likely to bolt unless it is attacked directly.