  It was only sheer luck (the death of the Khan) if medieval europeans weren't conquered and slaughtered in a great part by the Horde, changing completely our history.   -I don’t believe it would be possible for the Mongols to conquer Europe, no way there are to many variables working against them.     1) Mongols are good at Cavalry Warfare-Flanking, but Western Europe is not a good place for either of those things. What would they feed all those horses with? How well would those Horses perform in the thick forests of Europe? The main advantage of the Mongols is there tactics, none of which would work very well in Europe.   2) Europe is way to mountainous, well the Mongols where able to control other mountainous areas in the world like Korea, those areas are a lot closer to there base of Operations. Western Europe is a lot bigger and more populated, then Korea.   3) Mongols are over stretched, operating thousands of miles from there homeland, with few troops, and no friends, everybody at this point hates the Mongols, Muslims-Chinese-Everybody Else. The Mongols cannot go on expanding for ever; there Empire is too un-stable to allow massive new conquests, and there Empire degenerated rather quickly after this point.  4) Europe is way to Militarized-independent, Europe is crawling with castles, and a huge percentage of the male population is under arms. Historically a significant amount of Castles and fortified areas in Hungary resisted the Mongol invasion, the Mongols where only able to conquer the country side; the Carpathian Basin is a better Cavalry territory then the Alps or the Black Forest.   5) Mongol bows-The Weather of North Western Europe, would have affected them…..What would the Mongols be with out there bows? Would a Mongols beat a heavy armoured Knight with out the advantage of a bow? I highly doubt it.