For thousands of years people who lived near the Eurasian steppes like in Russia or China suffered immensely from raids and invasions by steppe tribes. Those tribes had powerful composite bows made from commonly available materials (wood, sinew and animal horns) and could use them from horseback making them very powerful and mobile fighters.
Did the people who got raided adopt the bows and horse archery themselves? The bows alone would have been more affordable than the horses.
Many of of the neighbours of the steppes adopted both the composite bow and horse archery. This includes Korea, China, Tibet, Russia, and India. The composite bow was also used for other than mounted archery, for example seeing use as a naval weapon (e.g., by the Ottomans, Koreans, and Chinese).
The Japanese adopted mounted archery, but used a long laminated wood and/or bamboo bow rather than the horn-wood-sinew composite bow.
When neighbouring settled peoples adopted the composite bow and mounted archery, there was typically one key difference between their practice and that of the nomadic herders on the steppe: among the steppe herders, mounted archery was a widespread skill, learned from childhood, while among the settled peoples, it was a specialised military skill, learned by soldiers (and sometimes only the elite soldiers), sometimes only beginning as adults. As a result, mounted archers of the settled peoples were sometimes lacking in skill (in both archery and horsemanship) compared to steppe peoples. This left the settled peoples with a difficulty: since inferior skill suggests that equal numbers and equipment is insufficient to reliably defeat steppe armies, how can they reliably defeat steppe armies? Some approaches that were used:
Superior numbers. While the supply of horses might make it difficult to field larger cavalry forces, settled peoples could often field larger armies.
Mounted archery as a component of combined arms armies. This is, of course, combined with the above point - the non-cavalry components of the combined arms army is where the superior numbers lie.
Weapons that are effective against mounted archers. The above two points implemented in the form of armies with swarms of spearmen can result in very large armies that are completely ineffective against forces of mounted archers. To make the above two points useful in practice, it is important for the army to include weapons that are effective for countering mounted archers. The ancient Chinese anti-horsearcher weapon was the crossbow: longer-ranged, it allowed infantry forces to be relatively safe from the enemy. In later times, the musket and cannon were added. Defensive weapons that were used included armour and fortifications.
Use of the above three steps could result in armies that were very difficult for steppe armies to defeat. However, with large infantry (and often artillery) components, it could be very difficult for them to destroy steppe armies. While they could defeat steppe armies in battle, it was often a simple matter for the steppe army to retreat if defeated, or simply to avoid battle in the first place. The chance of effectively defeating a steppe could be increased by having a larger and stronger cavalry component. Since the effectiveness and size of cavalry forces that could be raised from settled peoples was often limited by the availability of horses and the lack of strong traditions of horsemanship, this was often done by a fourth approach: