As things currently stand, horse archers are able to turn nearly 180 degrees to either side. This, in effect, means that they are able to shoot anyone around - or even behind - them. Meanwhile, lancers and other melee cavalry are restricted to a narrow ~45 degrees on either side. They can't even attack directly left or right, let alone behind themselves. I'm a cavalry player, and even I agree with this restriction. It forces cavalry to time their attacks and maneuver their horses more carefully. They have to charge infantry head-on, and if they are being pursued by enemy cavalry, they have to find a way to turn around before being able to attack.
On the other hand, horse archers can attack infantry from nearly any position. Some horse archers occasionally make 'strafing runs,' charging at infantry and firing as they pass, but more often they circle endlessly and spam arrows. Unless they're incompetent enough to move into melee range, they're completely untouchable. This is true even for enemy cavalry. Being able to turn and fire at pursuing cavalry makes the prospect of trying to chase them down laughable. Even if you're faster or more skilled at riding than them, you'll almost certainly take several arrows before reaching them - at which point you'll be at point-blank range and even easier for them to hit.
Horse archers should be subject to the same restrictions as melee cavalry. This would allow for fairer fights between cavalry, and would force them to be facing infantry if they want to fire on them. Rather than circling and spamming arrows, they would have to either stand still while firing or be charging in the direction of the enemy. This would eliminate arrow spam, since they would have a reduced window of opportunity in which to fire - after which they would have to re-orient themselves for another pass.
