How to fight Horse Arcehrs?

[Cambyses]

One trick I learnt is that if you can catch and engage one or two enemey units then nearby enemy horse archers will sometimes charge into the melee to try and assist their buddies. This is great news as it means you can start the hand to hand stuff before the AI has fired off all its arrows. Some of the best units for the catching bit are the archer/lancer types, but the better armed skirmisher cavalry are actually very good at this as well because their armour protects them from arrows, while they also tend to be very durable in melee. Although that is probably more a tactic to use against the Getai and Sauromatae due to the availability of suitable troops.

[fallen851]

Use Nizagan-i Eranshahr (Persian Archer-Spearmen). But really, any cheap ranged unit will do. Also for melee units, use large groups of units (240 men per unit) of spear men. These are effective because the horse archers will simply run out of arrows before they kill the unit, even if the spears can't force melee action initially.