Traditionally the horse was used to provide mobility: the archers would get close (required due to the smallish bows they used), unleash hails of arrows, and use their horses to escape if Infantry tried to close the gap. I'd say range 3 max, no charge ability (since they, from what I can remember, never carried spear or lance nor used the tactic), chance to panic like archers if they reach rearguard and are threatened by melee, perhaps give them the ability to fall back two spaces "riding at a gallop" set so that they pull back if an enemy melee unit can engage with them next turn. Basically they'd ride forward, start shooting the first target they can, and retreat if threatened with close combat.
