In many different places and at various times there have been hordes that relied heavily on mounted archers. Examples being the Huns, mongols, and various other Turkic groups that dominated the steppes on various occasions. These warriors were so effective that many empires collapsed or nearly collapsed when faced with such enemies. Why were empires defeated time and time again by this type of enemy, even when they had faced and defeated similar enemies a few hundred years before?
While not exactly an answer to your question this two part answer by u/wilymaker touches on the spirit of your question, but is missing some of your specifics.
Likewise this answer u/draculasaurus_rex touches on their success and some reasons for it.