You seem to be capable of engaging your horse in combat while mounted if you shoot a bow while riding it.
While attempting to hunt I shot an additional arrow at a fox that was dead and the projectile seemed to hit the horse (or near) I was riding. This caused the horse to engage me in combat while I was riding it. It didn't buck me off so I rode it near a cave and dismounted it. The horse was leashed and would not attack me unless I unleashed it. Managed to disengage combat by unleashing and running into cave.
Some notes
- Was dragging a cart
- Horse only had combat stance while I was mounted
- While leashed and off mount horse had non-combat stance and followed in caves normally