Horses.

[Outlaw Josey Wales]

They could always treat them as a 1 strength HQ unit. But, if you dismount, then you should have your 6 point cav dismount as a 5. If you want that 1 for offense or a 6 instead of a 5, they could have the choice to abandon the horses. As long as they are tethered to the horses, they can defend ad retreat, no offensive capability. Abandon the horses, they become a 1 strength inf and do everything it can do. If they abandon the horses, they go on foot with their mounted strength.