No culture has done so since the Mongols created the Yuan Dynasty and defeated the Jin & Song some 800 years ago. Even then some might say that the Mongols were lucky: the Jin Dynasty was at war on two fronts to the north and south, and the Song Dynasty had an incompetent military compared to its other grandeur attributes. Couple that with both Dynasties using gunpowder for the very first time, 500 years before the Thirteen Colonies battled against the might of the British Empire or Napoleon stomped throughout Europe, so there were bound to be difficulties in its application for warfare.
The Mongols may have achieved it on horseback, but we're talking about one of the greatest military empires that even had Europe quaking - it took the natural fortification of the Himalayas to stop them from invading India earlier on throughout their various empiric lifespans. The fact that they were nomadic in nature and lived primarily on the steppes while having to invade China through dry locations (such as the Gobi Desert, the Taklamakan Desert, and the Tibetan Plateau) that they were used to more than likely helped immensely.
As for recent history, Japan tried but failed miserably spending 8 "official" years with invasion plans reaching back to almost 15 years, and they still barely managed to get through north-east China throughout that length of time outside of a few coastal points here and there.
Disregarding all external facts of warfare and population of enlisted troops, the country itself is too large and too diverse in locale. It would be akin to invading North America collectively.