The struggles of armies invading Russia during the winter from Napoleon to Hitler are well-documented, but I've never really seen any mention of the Russian winter playing much of a role during the First World War.
Part of it is probably that the Eastern Front in WWI tends to get ignored in my country (the United States), but were there other factors, such as better German planning and preparation or less severe weather during the winters of 1914-1917?
For all the fame accorded to "General Winter" in the defeat of invasions of Russia, the General's record is quite mixed. Napoleon's Grande Armee crossed the Niemen on 24 June and tried in vain to catch the Russian army at the frontiers. By the time the chase ended in the Russian proper at Borodino in September, Napoleon's logistical arm was a complete wreck from the unusual heat of the Russian summer and forced marches. By the time the French left Moscow in November it was a broken force, and the Russian winter compounded the difficulties of retreating over an area that had been twice picked over during the summer campaign. Likewise, Barbarossa started in June, and began to sputter out around November due to the autumn rains and Soviet resistance. The fact that despite massive prisoner hauls in the cauldron battles of the summer, the Soviets could field a sizable force in the autumn meant that German quartermasters in Poland had to decide between supplying the overstretched front with bullets or winter clothing, and not surprisingly, they chose the former. Winter added another layer of misery for the Axis invaders, but it was Soviet resistance that stopped their offensive, not the snows.
The winters in the Eastern front also played a role in adding to the overall misery of the war experience, but like earlier conflicts, it was an adjunct to fighting, not a force by itself. Things became even worse when winter fighting met mountain fighting. This was seen in the various Carpathian offensives and counter-offensives. The Russian siege of the Austro-Hungarian fortress of Przemyśl prompted a counteroffensive in January 1915 and poor preparations on the part of Conrad von Hötzendorf led to frostbite and hunger being a normal part of KuK routine, and contributed to the inability to relieve the fortress, which fell in March. Likewise, weather conditions during the Ottoman-Russian clashes in the Caucasus in December 1914-January 1915 made things quite difficult. But it should go without saying that any military action in mountain ranges during winter is going to be hard on the troops.
Although most fighting was not in Russia proper during the First World War, there was one case where winter contributed to the course of events: the February Revolution of 1917. As temperatures plummeted and prices skyrocketed in Petrograd during the winter of 1916/17, winter exacerbated the tensions between the tsarist government and the urban population of the capital. Shortages were acutely felt in large families and the winter conditions strained the already overburdened rail infrastructure of many of Russia's cities, not just Petrograd. But as in other examples, General Winter was only a lieutenant to other phenomena. The breakdown in bread prices and transportation was a reflection of the lack of proper management by the tsarist authorities and mirrored larger problems in a near-dysfunctional state. Winter weather was another stressor on an already tense political situation, and these conditions would have continued to exist even had the weather been mild.
For all of the drama of images of snow-swept Russian battlefields, the actual immediate importance of the Russian winter is often overstated. This is no accident. Both Napoleon and a number of French writers ascribed defeat in 1812 to the winter weather, which was a way of covering up French mistakes in the campaign when the weather was warmer. For memories of 1812, exaggerating winter's importance added a romantic gloss and turned 1812 into a tragic defeat. Likewise, German generals after the Second World War would blame the advent of winter as magnifying Hitler's mistakes. Such narratives eliminate their Russian foes as active agents in their own victory. Winter made combat conditions more miserable for the common grunt, but such misery often cuts both ways for both invader and defender.