I don't know. As
@Bonyduck Campersang and I pointed out, there notably more widespread than that.
BUT in every case, mounted archery became a useful military skill only among people who had either a pressing reason to spend their time learning (like pastoral herders protecting their flocks and herds) or lots of time due to someone else supporting them (aristocracy or professional warriors). To take the examples mentioned:
Japanese mounted archers were either Samurai or monks, in both cases paid by daimyo or the monastery to do nothing else, or to treat the required skills as devotional.
Korean mounted archery was in answer to their neighbors to the north in Siberia/Manchuria, who were part of the central Asian pastoral tradition of mounted archery as a Way of Life.
The North American mounted archers were Buffalo Hunters primarily, a beast so big and dangerous that the preferred method before they had horses was to stampede a Buffalo herd over a cliff with the threat of fire. Archery from horseback was both safer and more efficient. The Commanches, by the way, were more famous as mounted lancers than archers, but like everyone else, they didn't usually try to spear a Bison, which was only likely to annoy him enough to turn around and stomp you and your horsey into paste.
Jewish mounted archers were foes of nomadic (Arab) mounted archers on the borders of Judeah, and so adopted the technique for the same reason the Koreans did.
Other places where neighboring groups adopted mounted archery in answer to their aggressive neighbors include the Russian city states against the post-Mongol Great or Golden Horde ('Tatars') and early Polish and Hungarian light cavalry against Turkish and steppe nomad groups of raiders. BUT in both cases they quickly abandoned the expensive and time-consuming mounted archery for either mounted lancers or gunpowder weapons.
AND in every case where mounted archery was 'nice to have' but not considered Necessary, the answer was to hire
them instead of trying to train them domestically. First, because the combined skills of riding and archery both required a lot of time and practice so the practicing people had to be fed and maintained by someone else, and also because keeping horses required a lot of land that would not be available to feed people, making the mounted archer a
very expensive unit for settled, city-based (i.e., All Civs as the game represents them) cultures.
If they had enough reason and enough Gold they could hire quite a few of them, though. The Byzantine armies under Belisarius in Italy and Africa consisted almost entirely of a strike force consisting of cataphract heavy cavalry and hired Hun horse archers. In the
Notitia Dignatorum of the late (post-Attila) Roman Empire, they list numerous auxiliary units of
Equites Sagitaria Hunnae : mounted Hun archers - one of which was stationed in Britain, which probably produced some serious 'culture shock' on all sides there!
For game purposes, I suggest that the mounted archer be a 'Barbarian' or Non-City-Based Group unit, but available to hire as mercenaries (and Hear Me, Firaxis, Civ VII Needs A Mercenary Mechanic in General) by any nearby Civ with the Gold.
