It's not really nerfing that's under discussion though. Just changing what the challenge is. And the doomstack as is, seem to be a sub-optimal mechanism. I'd agee that the Hordes should be both terrifying and, well... horde-like.
Ironically, the word "horde" invokes the idea of nigh-limitless numbers and senseless aggression. In reality, the source of the word was often outnumbered and tactically rather sophisticated (for the time).
The question is, can the AI manage a historically accurate horde in a way so as to remain a suitable threat? I rather suspect no, but it's a problem worth tackling.
From some more cursory research on the internet, it seems like mongols used a larger proportion of heavy cavalry than they are represented as in game. Wiki says a mongol force was 60% light cavalry, 40% lancers. Even assuming Wiki has their sources correct, that would probably be more of a guideline than an on-the-ground reality. A mongol Tumen might have a paper strength of 6000 horse archers and 4000 lancers, in reality that number would vary reflecting losses in the field and be augmented by forces from subject states. Presumably subject nomadic tribes would supply mostly horse archers and light cavalry. Infantry and seige contingents were deployed too, but could the AI handle the combination? I rather think that it would fall into the trap of consistently letting a slogging mass of infantry and archers negate their mobility advantage.
A cultural-specific boost to the hordes cavalry units, as well as special tactical choices reflecting their tactics, might be able to make them threatening even without doomstack numbers.