Just curious, do you have any info related to this? I'm not offensive or being rude against your opinions/thoughts. Just asking with hunger of knowledge. Because as far as i know Steppe warriors/invaders from Asia/their empires didn't fall apart because of battle losses but dying of a khan/things happening in their homeland (like succession etc).
Don't worry, no offense taken.
I consider myself a reasonably well read economic and political historian, with LOTS of time spent reading and or modelling all aspects of medieval and ancient farm economics. It all started in the 80's when I got tired of the blatant unreality of Dungeons and Dragons (I never really associated much with fantasy), I started looking up WHO stats on farm economics, then turned to the Domesday book (and various other references analysing the data from it), followed by personal Excel simulations and RPG / manorial campaigns that I ran for my friends.
First off, note that pound for pound horses generally consume around twice the grain that oxen and cattle do. It all depends upon your terrain etc of course, but in general you could run four sheep on one acre or one cow/ox on four, horses require around 8-10 acres of grass, fescue or (in the most extreme cases only) grain. This is why medieval farmers (at least Western European ones) generally used oxen rather than horses for ploughing and hauling wagons - they are cheaper to run. On the other hand, if land is cheap/free then horses are far better as they are generally faster in all respects, even when carrying out manual labour, eg ploughing etc. This is why after the Black Death Europeans generally turned to horses for farm labour as cleared land suddenly became very cheap - losing 30% of your population will do that for you !
In Western Europe at least land was generally cheap, but CLEARED land was at a premium, so devoting large regions to support horses was a luxury that could only support fewer well trained and well fed horses, thus the western emphasis on heavy knights and lancers as opposed to masses of light cavalry. As with every rule of course there are exceptions - it is no accident that regions like Hungary, Spain and North Africa produced qood quality light horse - there just happens to be more freely available open grasslands in these areas.
The second point is that battles in the wide open spaces tend to place a premium on ranged weapons and mobility, while those in tighter terrain emphasise skill and training, armour and heavy weaponry. Place 300 Spartans in a mountain pass and nothing will break them, but put them in the middle of the Ukrainian steppes and they wouldn't last 30 seconds. OTOH, place 300 horse archers in that mountain pass and the Spartans would roll right over them, put them in the steppes and unless they wanted, you would never even touch them.
I recently watched a series on knights, the show was originally German production with English overdub, being Germans they did lots of tests on armour, weapons etc. They tested the legend about Crecy and Agincourt that the English longbows could pierce plate armour and found that steel tipped bodkin pointed arrows BOUNCED off 4mm steel plate at 50 yards. Shots through cracks or that hit chain mail could generally penetrate up to 15 cm, so archery IS effective, just not as much as we always read and see about.
The bottom line here is that horse archery is great against a fixed foe that has lower mobility and that can't use its shields to good effect (ie flank or rear shots), but against the same foe in tighter terrain ie the type that generally prevails in western European woodlands and farmlands is MUCH less effective.
Thus my point about Altaic peoples generally adopting armoured horsemen and close order infantry (just like all the other feudal realms of western Europe) once they left the plains.