From an earlier answer of mine

The Russian winter certainly did make offensive operations quite difficult for the Germans in 1941. Extreme cold degraded the combat performance of the army as a whole. Vehicle engines were difficult to start in the cold, personnel wastage increased to frostbite and other problems, logistical resupply was easier than mud of the autumn Rasputitsa, but it was still difficult. Added to this was the morale problems the onset of winter engendered as the Soviets appeared no closer to collapse. Bread rations not only froze, but the snows summoned up images of Napoleon and other failed invasions. But with that said, "General Winter" did not discriminate between sides; many of the weather-related problems the Wehrmacht encountered in 1941/42 were also found within the Red Army as well. Some Soviet equipment was better for winter conditions than German ones. Soviet felt boots were better than the hobnailed German jackboots. The Luftwaffe often had to fly out of captured or extemporized airfields which meant that they had to operate in the cold to the detriment of operational reliability while Soviet aircraft operated out of established airfields. The same problems impacted the operations of German panzers and motorized transport as winter conditions made it hard to start engines and added further headaches to an already stretched logistical system.

But winter conditions often cut both ways in the war. The average Soviet soldier had the same biological response to cold as their Axis opponents. Hobnailed jackboots might have been more conducive to transmit cold to the toes than felt boots, but frostbite was still a major concern for the Red Army accounting for between 2–4% of the combat surgical trauma according to one estimate in Military Medical Research. Some Soviet equipment might have been more robust to handle lower temperatures, but this discrepancy was not huge. The problem for the Germans was not winter but rather that intensive military operations continued through the winter season.

Many of the Heer's general officers had experience with the climatic conditions of Russia during the First World War and many of them were aware of these difficulties. However, both the OKW and OKH planners for Barbarossa planned to defeat the bulk of Soviet armies before the onset of winter. In January 1941, Luftwaffe quartermaster-general, Lieutenant-General von Seidel met with OKH head Halder in a conference coordinating the supply situation between the Heer and Luftwaffe, von Siedel broached the topic of winter clothing, his Heer counterparts tersely noted that the campaign would be finished by winter. For the most part, the German military establishment took a cavalier approach to the capabilities of their Soviet enemy and their thinking mirrored that of Hitler- that one swift kick would lead to a collapse of the Soviet state. The campaign planners anticipated that the winter of 1941 would mostly be a mopping up operation whose troops would require a minimum of supplies.

This massive underestimation of Soviet capabilities led to a disaster in late 1941 as the logistical system of the Wehrmacht began falling apart at the seams. Not only had the Red Army continued to fight despite massive losses in the various cauldron battles, but Barbarossa's logistical network was incapable of adequately supplying the German armies in the field. Instead of mopping up, German troops were engaged in offensive operations in November 1941 that ate up equipment and ammunition at a prodigious rate. In such a overburdened logistical system, winter clothing often had a lower priority than fuel or ammunition and sat well behind the lines in supply depots in Poland and the Western USSR.

In short, the "titans" of the German General Staff were in a dire situation of their own making. Their planning for Barbarossa was careless and they brushed aside inconvenient details that suggested defeat of the USSR would take more than a single campaign. Victory over France in 1940, which few officers in the Heer had actually expected, had engendered a fatal overconfidence which dovetailed with other problematic components of the German way of war.

But in one small way, the German planners of Barbarossa managed to wring a victory of sorts postwar by foisting all the blame for the campaign's missteps upon Hitler. This narrative stressed Hitler's tinkering with the campaign such as encouraging a drive towards Kiev that meant Moscow was only within reach of German arms by November. This and other alleged missteps by Hitler- who, let's be clear did make mistakes but also with the collaboration of OKW/OKH- meant that the Germans ran out of time in 1941. Such a narrative places responsibility of weather for defeating Germany not on the fact that the USSR had mobilized a staggering amount of troops since the onset of the invasion. The already common trope in the West of of Russia's General Winter (which itself is not true- Napoleon's Grande Armee was a defeated force by the winter of 1812) lent this distorted and selective memory of 1941 a degree of legitimacy.