Horse Archers are fast, versatile units that can harrass and easily pick off most armoured units in particular at ease. They can also fire whilst riding which can make them a nightmare to fight off unless you have a group of bigger horse archers that can also fight back. They do however have a slightly faster reaction time whilst stationery, although their reaction time is one of the fastest in the whole game regardless.
These units are ideal for encircling and harrassing enemy units, because almost all units will struggle to reach them, even Knights whilst mounted. Light Cavalry can catch them in terms of speed, but their armour is so weak, they will virtually always die a long way off being able to do so unless in a very large group.
Once you actually catch up with them, they are virtually useless in melee combat and their entire use comes from running enemy troops around in circles and constantly firing on them. Crossbow bolts and other missiles can do great damage to Horse Archers, however with their fast movement you can quickly pull them out of range of the enemy units, whilst still firing on them.
You can recruit Horse Archers from the rank of Earl. You will need 80 gold as well as 2 Honour and 1 peasant from the campfire before you can recruit a Horse Archer. Honour can be produced by the means shown in this article.