Those are quite real. Large-scale warfare has always been above all about logistics - to put it bluntly, keeping your soldiers fed, clothed and generally supplied and alive.
Which gets pretty difficult when the supply columns (and for that matter, combat troops) can no longer move owing to the roads having turned liquid, engines and pack animals freezing, men and beasts starving and losing bits to frostbite, heck, even weapon mechanisms freezing solid on a bad day.
Just as an example, when the Germans were checked at the gates of Moscow a very important factor was their logistical chain pretty much collapsing in the early winter weather. Hard to keep fighting at peak efficiency when the fuel and ammunition and w/e plain isn't getting through because the supply trucks and carts are stuck in cold mud, tanks refuse to start in the cold, lubricants freeze in guns and soldiers keep having their fingers fall off...
(Similarly, in the monumental cock-up that was the Soviet first-phase invasion of the Winter War the hapless Red Army troops trapped in the forests of Finland suffered at least as direly, as their supply lines were flatly cut and the winter was of record ferocity.)
On the same vein Napoleon's army more or less starved and froze to death under him. Not that the Russians weren't only too happy to add to the misery and attrition by stepping up their raids and harassement the second they realized the French were screwed...
Comparable cases can be dug up from any number of wars. The cold may be absent owing to geography, but the overwhelming importance of keeping armes supplied - one way or another - remains.
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