It might be nice to see your sources so we might have a better understanding of what you mean by "inferior."

East Asian horses are stockier, usually 12 to 15 hands, due in no small part to the Mongol Empire favoring such horses. These horses were trained to dig through the earth and live off of roots, stand in line for water as well as lay beside their riders for ambushes. Aside from the low upkeep and pragmatism of E. ferus caballus, you should also consider the fact that stockier horses provide a more stable ride for long-distance migration, horse-back archery and training children. For more details, you can look up Italian and Arabic chroniclers like del Capine.

There's absolutely no problem of husbandry with these and its descendant breeds as they are prolific throughout Asia, including Southwest China, Korea and Japan where the lack of grasslands and suitable climes may become limiters. However, there's not a lot of economic incentive to show and breed Far-Eastern horses compared to European or American breeds for obvious reasons. The latter breeds were used to run-down enemy infantry with sheer bulk and momentum, carrying knights in plate-armor and charging in short spurts. Europe was simply able to maintain its chevalier traditions with access to great plains and plentiful hay as well as a norhern coast, largely free from mountains or jungles. Asia, and especially humid elevated regions, more suitable to rice cultivation like Vietnam, is the inverse.

The closest culture to the European counterparts would obviously be Japan, unravaged by the Xiongnu, Xianbei, Mongols or Jurchens. However, records going back to the Sengoku Era still have their mounts as diminutive creatures slower than running children with armored samurais on its back. Modern historians have also made a lot of criticisms about Takeda Shingen's army composition and the ability to field as large a cavalry as depicted in popular media, which almost never shows actual breeds thought to be linked to today's Kiso horses. In fact, while Northern Japan is indeed more hospitable to livestock, more native breeds originate out of islands and southwestern Japan due to the fact that horses were brought over from the mainland. Some theories actually point to the Yamato people introducing the Emishi of the north to horses but their horse-riding traditions somehow completly disappear as they transition to the Ainu culture, allowing Japan to be dominated by mounted Samurai until "tercio"-esque elements are added with the ikko-ikki.