>>530386889
Their population has a hard limit parallel to how many horses there are in our timeline.
As you very well should know, raising a horse, much less an army of horses, then sustaining them in the field, is incredibly logistics-heavy. There were entire organs of state dedicated to running breeding programs back when cavalry was still relevant; those have obviously gone by today.
Their incredible logistical needs pretty much ensures that in a pre-agricultural revolution world umas were always gonna need the more numerous humans to produce sufficient food.