Not necessarily. The Rus princes struggled to mobilize in dead-of-winter against the Mongols in 1241, resulting in each being isolated and defeated in turn, frequently with little to no warning.
The first leg of his winter retreat, from Moscow to Smolensk, was the worst part and cut his army of 100,000 in half. But prior to winter, from late June (invasion start) to September (Borodino), Napoleon's Grand Army lost 450,000 troops (out of 600,000 at the start line) to a massive typhus outbreak.
Kinda puts the whole "General Winter" thing in context...
Sturgia used to get a snow bonus that was outright overpowered. Their parties would be like 1.2 faster than everyone else from the same/similar starting point so it was legitimately dangerous to raid Sturgia in the winter. And the winter in Sturgia stuck around for like a good five months.
That was quickly nerfed, then removed entirely.