Why does this seem ridiculous? Horses, unlike automobiles, get tired, injured, scared. One horse can only carry so much equipment, food, and water, plus a rider with saddle. I can't speak to Mongol society, but among many Native American cultures, horses were a form of wealth, and it was a point of honor to have many.

It's completely plausible, in fact even likely. Horse get tired, have different temperments, and get older. Having multiple horses for multiple tasks (Hard riding, pack horses, war horses, etc.) is quite a practical thing to have if you're a nomadic warrior society. In a somewhat related way, Comanches in NW Texas were not considered men unless they had at least 3 horses to their name, which they usually stole from Mexicans or Anglos or took them as prizes from slave raids on other Indian societies.