The top tier ranged unit for the Khergit Khanate.
Mounted on coursers, they are extremely mobile, but the combat AI does not use tactics that reflect their ability.
As opposed to static ranged troops that fire arrows at regular intervals, horse archers seem to randomly combine shooting, melee, and ramming (read as: dying). They tend to run around in circles without firing any arrows.
The advantage to these guys is that they're on horseback and thus don't slow down your army like any other archers would.
When closing, Horse Archers will usually attempt to fire, but terrain variations or obstructions may cause them to break off.
Because they have such fast horses, when charging, they will usually be among the first in contact with the enemy. Sword Sisters and Lancers have a similar problem. This is particularly problematic since coursers don't have much armor or hitpoints. Also as mounted archers they respond to "Cavalry Hear Me!" commands with heavy cavalry like Swadian Knights.
Note: In Warband, you may redesignate units by going into the party menu and clicking on "Class of troop"; and then giving them a new class, e.g. Horse Archers or whatever.