they should lower the accuracy a lot on horse archers when they move near top speeds. but they should also make them more accurate against sidestepping enemies. they dont understand mobility like foot archers and foot skirmishers do. their main focus should be distracting and skirmishing fleeing enemies, not being that lethal. that should be the other half of the army's job, the infantry and cavalry
their real issue is on the worldmap. they have too much speed bonus. they should have a huge speed bonus on clear grasslands and plains, BUT have a large speed penalty during winter, and a small penalty in forests and deserts. im assuming aserai horses are better built for deserts than nomadic horses. i dont see how horses move fast in snow overall
so they will only be very fast on the world map in certain areas at certain times like battania and sturgia. if i remember right they have 10% bonus in forests and snow, but khuzaits have 20% overall, meaning they are faster than battania and sturgia in the zones that they should be dominating. i mean isnt the whole point of battania and sturgias speed bonuses in certain terrain meant to reflect that they dont favor horses and have better mobility in those areas? besides their intimate knowledge of those areas