The only reason the Song dynasty didn't get to kick ass was because they lacked horses due to an idiot in the 5 dynasties & 10 states giving out the region that provided them to some Khitan warlord.

If the Song had horse mobility, they would have had offensive power, that could allow decisive strikes on hostile invaders. Lacking mobility, the Song dynasty could only drag around sluggishly their costly logistic lines and be forced into passive defense(but even in this weakened state, was still strong enough for Ghengis Khan to mind his space and back off).

If Song technology and economical power were paired with horse mobility, it would be possible that the Mongol invasions would never come to exist.