There were many ethnic groups in central Eurasia which followed a nomadic culture featuring light cavalry and mounted archery in war. Some were Iranian, some Ugrian, some Turkic or Mongol. Sometimes conquering hordes were ethnically mixed.
Mongolia may have had only a million people, but a much higher proportion of the population was available to fight than in (e.g.) Europe, and they were tougher than people of settled regions. Being nomadic, their entire population could move to support the army. Europeans, Persians, etc. could not compete with that strategy. Also, they had absorbed people from other groups into their conquering hordes. They were almost impossible to beat, and were stopped largely because they themselves became the soft, luxury-loving aristocracy in places like India, China, and Ottoman Turkey. The Mongols proper apparently became more peaceful after taking up Buddhism. (Timur was a Muslim, with all the propensity for violence and intolerance that entails; he performed his genocidal atrocities in the name of Islam, although he killed many Muslims.)
One well-known Turkic speaking group called Yakuts, or Sakha, have a Sa'ami "x-factor" genetic marker (and some other characteristics). These are the folks in the background of the Japanese ruling class as well. Otherwise they are identifiably Chinese but they herd cattle ~ unlike every other Turkic or Siberian group.
There were, for the most part, no Indo-European or Finno-Ughric speaking people in Scandinavia 5,000 years ago!