This is sort of a broad question, but I'm interested in how exactly the mongols came to become so dominant.
The impression I have from what little I've learned about them is that the mongols basically swarmed in with massive amounts of horse archers with little regard to tactics aside from 'shoot at enemy while riding towards them, run away when the enemy pursues, ride back towards them while shooting, repeat until enemy is dead or fleeing'.
Is this correct? If so, where did there get all the horses from? I remember reading that in europe horses were very expensive to breed and raise, and so only the wealthy nobles had access to them, who formed the bulk of medieval cavalry. So how is it that all of the mongolian soldiers had their own horses to ride?
The impression I have from what little I've learned about them is that the mongols basically swarmed in with massive amounts of horse archers with little regard to tactics aside from 'shoot at enemy while riding towards them, run away when the enemy pursues, ride back towards them while shooting, repeat until enemy is dead or fleeing'.
I recommend looking at /u/boooyyah 's link. There is good stuff there. But I also recommend looking at a general history like J J Saunders', History of the Mongol Conquests.
The Mongols were probably one of the best led armies prior to the modern era. Their generals (like Subatai) were nothing short of tactically brilliant. And they had instilled a level of obedience and such that certainly no Western army had. They regularly out maneuvered their opponents, and in Europe at least, regularly trounced armies much larger than their own.
You only need to look at the battle of Bardov. There they were outnumbered 3 to 1. Jebe and Subatai split off and hid a portion of their force and then lured the Georgians into a position where this hidden force could hit the Georgians flank. This the Georgians recovered from, but it exposed their flank to the main body of Mongols. And the Mongols took advantage, eventually driving them from the field.
Or look at Kulka River, where they spent over a week stringing a Russian force along. This broke up the Russians into a huge miles long column. Then the Mongols wheeled and hit the vanguard in a prepared battlefield where they had smoke pots set up to hide their numbers and maneuvers. They defeated the Russians, who outnumbered them massively, in detail.
Later at the battle of Mohi, the Mongols used naphtha and perhaps gunpowder "grenades" flung by siege engines to take an important bridge. And to distract the Hungarians while the main body of the Mongols crossed the river elsewhere. This allowed the Mongols to achieve an envelopment of the Hungarian camp. And then rather than assault the camp, they intentionally left a gap in their lines. When the Hungarians saw and broke for the gap the Mongols were prepared and they cut the Hungarians down.
In all the Mongols were an intelligent and incredibly adaptable foe. In fact they became quite adept at siege warfare and maintained a train of Chinese and Persian engineers. They definitely adopted gunpowder use in China, and may have used it in Europe and the Middle East (or that may have been naphtha, opinions are divided). The fact that they also had greater mobility and could perform hit and run tactics like you describe just made them more dangerous. But they had a whole lot more in their bag of tricks than just the "feigned flight."