The earliest large warhorses were a special breed (N...) from Iran/Persia and early lance called kontos were either from Greek/Macedonian in Bactria or Dahae, who were settled barbarians ruling over civilized peasants.
They can't really be considered barbarians in civ as the development required considerable state power and industry - cataphracts (prior to knights) had to be trained in rigid military formation (nothing like hunting), required combined arms, special horses and special armours (prior to mail). Scythians and later Sarmatians also controlled cities which can produce whatever not available on steppe.
Compare that to Xiongnu, who were really poor and denied access to even basic armor. The gap between settled and barbarians only grew wider since then. One missing piece in civ is the critical need for barbarians to trade with settled civilizations, without which their society could hardly function.
The Nisean horses were not particularly large in the sense of taller, but they were huskier and able to carry more weight, which is why they were desirable. The former belief that 'large' horses able to carry armored men only developed late in the game is no longer tenable, however. The earliest horses encountered by humans and hunted for food, later domesticated and ridden, included horses up to 14 hands tall from skeletal evidence, or in the range of modern riding horses or medieval Coursers. And the Scythian Massagetae are reported by eye-witnesses at Gaugamela (Ptolemy Lagus later of Egypt, in fact) as 'armored men riding armored horses' - cataphracts, in fact, although they appear to have been armed with lighter lances rather than Hetairoi-style Kontos ('barge pole'). Nevertheless, Scythian graves dated to the 7th century BCE have both native iron swords and daggers and 'spears' up to 3 meters long with heavy points not suited for throwing, which therefore must have been used in close combat from horseback. Since these are virtually identical in length and weight to a medieval European knight's Lance, it's hard to assume they weren't used similarly. The slightly later Sarmatians, also from the steppe, were armored men with long, heavy lances that were hired by the thousands by the Imperial Romans after they had to adopt special formations and include 'lanciarii' - pikemen - in the Legions to counter the charge of the Sarmatians when they weren't in Roman pay. Lanciarii Sarmatii
(Sarmatian lancers) appears several times in the Notitia Dignitorum
, the list of the units and auxiliaries in the Imperial Roman army, to describe auxilary cavalry of Sarmatian origin.
Be careful about assuming that the steppe warriors, from the earliest times, couldn't produce high quality metalwork. From 3000 - 2500 BCE pastoral metal-workers in the Yamnaya and similar pastoralists from the modern Kuban to the area of western Ukraine were producing high-quality tools and weapons in bronze, copper and early iron and decorative metal objects in copper, lead, silver and gold. Among other things, they produced bronze saws that allowed them to cut cleanly across the grain of wood and produce the first solid and spoked wheels and the light chariot, which was then spread from Central Asia to China, India, the Middle East and Europe (2100 - 1800 BCE, first spoked wheel chariots found in graves of the Sintashta culture, a pastoral group living north of the Caspian, by 1700 BCE the chariot had spread to Shang Dynasty China, by 1650 BCE to Egypt via the Hyksos from the Levant, by 1600 BCE the chariot appears in Mycenean Greece, by 1500 BCE spread to the Middle East via the Mitanni, whose aristocracy appears to have been Indo-European speakers off the steppes themselves, by 1300 BCE spoked wheel chariots appear in Iberia and Sweden, Poland, Germany and central Europe)
And the Xiongnu might have been poor, but the Chinese traded with them and the Yuezhi to get good cavalry horses and the Xiongnu Confederation beat the stuffing out of the Han Chinese armies in 200 BCE.
Absolutely agree about trade, though. The pastoral societies spread over wide areas of territory, which made them the consumate 'middle men' between settled cultures and the principle agents for moving goods long distances for profit. That dynamic appears not only on the central Asian steppes, but also in groups such as the Comanche of North America, who managed a 'trade empire' between the Mississippi valley and New Mexico that gave them access to industrial manufactured goods and also markets for their horses, because, like the Yuezhi and Xiongnu to the Chinese, the Comanches were providing horses for a nice profit to everyone from the native Americans on the plains to the north to the American settlers in (modern) Arkansas and Texas.
IF Civ is ever going to get pastoral cultures right - or at all - the trading dynamic has to be part of the model.