Most AI procedures that involve movement have a flag for RideHorseIfPossible. If this is set to true, the actor will ride a horse if there is one nearby that they have ownership of. While mounted, the horse is controlled by packages applied to the NPC. There aren't commands to force an NPC to mount and dismount, so for example in the first part you'll probably need to do a sequence of procedures, or phases within a scene, where:
1: the NPC travels to a marker with RideHorseIfPossible set to true
2: the NPC speaks their lines
3: the NPC travels to a second marker with RideHorseIfPossible set to false--this should force them to dismount and walk to that second marker