winter first — Kahn's army consisted mostly of light horse soldiers. they were from Mongolia and knew a lot about winter already. Thus, their campaigns were mounted only during the summers — they knew better than to campaign at any other time of the year.

Kahn's horse soldiers featured a lot of light archers. Those are wonderful troops [for hundreds of years ago] on the treeless steppes west of the Urals and east of the forests of the Ukraine. They would have all the advantages of speed, ability to hit from a distance, and mobility. Voila! they conquer Russia.

Just as they failed to go farther west, losing to the King of Poland and Lithuania. The joint nation [Poland and Lithuania] at those times included the western parts of the Ukraine and what i now Belarus [Belorussia on old maps]. This was forested country and the King kept his troops inside the forests where archery was severely impeded and offered his ground troops natural cover and defenses. The horses weren't very effective charging into the brush and so the westward progress of the Khan's armies was stopped.

The Russians threw off rule by Khan's successors within a few generations, in part [imo] because Russia was the poorest part of the empire. China was much wealthier land and thus drew the attention of the succeeding dynasty.

I could try to give a better answer but I couldn't other dude got it spot on.