One tested tactic to employ the veteran horse archers is not to charge directly, as it makes them get into melee with superior melee infantry/cavalry without using their formidable horse archer skills first.
Just form them up and get them follow you, reform them just behind a hill or equivalent, something that will make the enemy slow, also protecting them from the enemy archers, wait until the enemy units come within javelin range and then, attack. They completely avoid melee as they rush to the right flank hitting arrow after arrow and God! they ARE deadly with this tactic.
They continue to avoid physical contact until their arrows are depleted and charge at the now deformed enemy lines with the remaining troops scattered here and there, most of them wounded from arrows. The results are devastating!
They function properly if used right. If left uncontroled, they charge into enemy lines, 1-2 at a time, usually getting murdered by the massed enemies. IF they survive the forst melee action, they properly change to horse archering, but it's usually too late. Never charge them directly over long distances.
I find them extremely effective, and having a troop of 30-40 exclusively with vet HA, with high riding skills, accuracy on horseback and not too bad melee, chasing down everything on the map with superior speed, getting lot of casualties on the enemy without losing many of their own, leaving the player to choose targets as they completely deform the enemy lines
with their arrows and the enemy chasing them.
On harsh terrain, unmounting them gives you a lot of good and mobile archers, able to compete with the best the enemy can have, also they are VERY-VERY useful on sieges, especially on defence, since they can pepper arrows on the enemy inflicting heavy losses before switching to melee.
The game and it's troops are balanced very nicely, every side can win if used right.