This replaces the current mounted combat rules for Openquest, which are that someone on horseback gets a +25% to their attack and defense skills against non-mounted opponents, while the non-mounted fighting the mounted get a -25% to their defense rolls. I don't think this makes much sense, nor do I like having to add bonuses unless absolutely necessary. There's also a rule that limits the maximum effective score of combat skills while mounted to the score of the riding skill, and I hate those kinds of rules.
Things I want to incentivise:
Charging on mounts
Attacking and/or killing mounts
Therefore I propose the following rules, which completely replace the mounted combat section:
Mounted attackers increase the damage of their attacks to the next largest die type.
Riders move at the speed of the mount they are riding. They use their movement action to guide the mount.
When a rider's mount is dealt damage the rider must immediately test their Riding skill or the mount's persistence (test only one). If they succeed, the mount does not panic. If they fail the test, the mount uses the Flee Combat action until either the rider regains control (they may test each round) or the mount cannot see or hear the attacker.
Bonus alternate rule:
I don't use weapon sizes or the associated rules because I find them fiddly, but if one wished, instead of increasing the die type, one could increase the size of the weapon by one size (Small weapons become medium size, etc.) when attacking.