Well, General Winter is much more powerful if your equipment doesn't work in subzero temperatures and you have huge supply chain bottlenecks that make it hard to supply fuel and winter clothing.
groups like the mongols easily took rus lands and burned kiev because of their protection against the mentioned problems. Steppe horses and soldiers were good in the cold, their tools were working just fine, and their raiding of cities like kiev made it easy to just not need supply lines.
Mongol horses eat all the food in an area, they have to remain mobile.
They were easily defeated (2nd time around) with area and food denial methods like castles.
The easiest direction to attack Moscow is from the south. Woods West of Moscow were intentionally left untouched for centuries to be a deathtrap for potential invasion.
None of these factors are at play here.