As part of our theme here of defending Western civilisation and the Western, especially Northern European people, note is made of and informative discussion at Quora.com by Tim O'Neill, "Did the Mongols Have a Reasonable Chance of Conquering Europe in the 13th Century, had Ogedei not died just before launching his invasion?". O'Neill argues that the Mongol's would not have conquered Europe. There are a number of reasons why, including geography, logistics, historical precedents; Western European strategy and tactics and politics.
Beyond the Hungarian Basin there was simply not enough pasture to sustain horse battle tactics that the Mongol's used. Europe in the 13th century did not consist of open countryside but rather of thick forests which was not suitable for horse nomad battles. The armies of feudal Europe were battled trained in their enclosed environment. Castles dotted the landscape, so the Mongols would have had to destroy these castle-by-castle, which would have been an impossible feat given that the number of castles at that time were in the tens of thousands. The Mongols in the Golden Horde campaign of 1285 in Hungary were worn down from attacking castles, and retreated. They in turn were attacked by Ladislaus IV and destroyed.
Europe was divided politically at the time, but even this would not have aided the Mongols because fragmentation meant that, unlike in China, there was no central capital to defeat to capture a territory. Further, Mongol invasions would have united Europe against a "pagan" for threatening Christendom; Western Europe had, after all, conquered territories in the Middle East during the Crusades.
O'Neill concludes that all of these factors, combined together, makes it highly unlikely that the Mongols could have just rolled into Europe. Even under the influence of Christianity, this was still a highly warlike people who had 300 years previously produced their own "hoarde", the Vikings, who were probably more fierce and dangerous than the Mongols. It is highly doubtful in the hand-to-hand melee battles that Europe would entail, that the Mongols, primarily cavalry warriors, would have defeated the West as they did China.