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.
During WWII, the two rasputitsa/mud seasons generally were the only times the eastern front was slightly quieter and these seasons significantly impacted both sides.
Summer and even Winter generally saw numerous offensives by contrast.
During the first year, in October 41, Barbarossa and operation Typhoon (Battle of Moscow) stopped temporarily in part due to the rasputitsa, and only resumed when the ground froze in early November (incidentally giving time for the Soviets to reorganize the extremely weakened front protecting Moscow).
The soviet Winter offensives mostly stopped around the Spring rasputitsa, Case Blue and other initial battles only started only in late April 42. and after Stalingrad, the Soviet reconquest of the South during the 42/43 Winter stopped again around Spring 43, with offensive operation only restarting in July 43 (Battle of Kursk).
There are of course many other factors explaining these pauses (offensive strength exhausted, over-extended supply lines, etc), but rasputitsa was definitely a factor.
I didn't imagine the spring being the best defence against the east.