"Russia" as a singular political entity did not exist in the 13th century. What most people are talking about when they talk about the Mongol invasion of "Russia" is Mongol actions against the principalities of the Rus', an area that covers parts of what is now Russia, Ukraine, and Belarus. The main power in Rus' was the Kievan Rus', a loose federation of multiple towns and cities, not a centralized kingdom.

The Mongols succeeded against Rus' partially because of this disunity - Kievan Rus' had been on a decline even before the Mongols had arrived and therefore the initial Mongol invasion under Batu Khan basically involved defeating several separate principalities that were mainly focused on defending their own cities. Batu Khan sent different Mongol commanders to attack a variety of places at once, which kept the principalities of Rus' from presenting a unified force against him. Thanks to possessing the usual traits associated with the Mongols at their height - superb leadership, a stunning ability to conduct fast maneuvers and coordinated movements, and foreign expertise to help with sieges, the Mongols triumphed decisively.

In the history of Mongol expansion, Rus' was not a particularly difficult place for the Mongols to subdue and was really just one part of a greater thrust into Eastern Europe.

Part of what made Russia so difficult to conquer was the harsh winters, this however wasn't such a factor for the Mongols because the Mongols were used to colder. Winter was their favourite time for campaigning.

January in Novgorod (capital of the Kievan Rus) has average high/mean/lows of -5.9/-8.9/-11.6 celsius meanwhile Ulanbataar (current capital of Mongolia) has January averages of -16/-21/-26 celsius. Russian winters are like Mongol springs (March temp ranges from -1 to -14)