I think in asking this question, you severely underestimate the Russian winter. Although I can't specifically speak for earlier campaigns, like Napoleon's, I should be able to describe how it was in WW2. Let's take Stalingrad as an example, which is situated in the south of the country, on roughly the same latitude as Paris. During the battle of Stalingrad during the Second World War, fighting went on in and nearby the city from the German advance to the Volga in the Summer months of 1942 through the winter into spring of 1943.

There are no records for temperatures in Stalingrad for the winter of 1942-3, but there are records for Oktyabriskit Gorodok, around 300km North of Stalingrad. The average temperature was around -17.8C (~0F), but was reported to reach around -30 to -40 on some days (-22 to -40 Fahrenheit). Imagine being stuck outside with no real shelter other than trenches and bunkers, with no proper winter clothing for weeks on end- this was the Wehrmacht's situation. This kind of cold winter is significantly harsher than in the rest of Europe, except maybe parts of Scandinavia. Meanwhile the Russians have lived through harsh winters all their lives, know how to survive in it, and have proper winter clothing.

Vasily Grossman, a war correspondent for the Red Army newspaper Krasnaya Zvezda, who was very popular among the common Russian soldier, wrote as he advanced with Russian forces surrounding the Germans at Stalingrad: 'It is severely cold...Snow and the freezing air ice up your nostrils. Your teeth ache. There are frozen Germans, their bodies undamaged, along the road we follow. It wasn't us who killed them. The cold did. They have bad boots and bad coats. Their tunics are thin and look like paper.' The Germans' bread was frozen sold so became known as 'eisbrot'. On 20th January, Sixth Army HQ reported that 'there is not a single healthy man left on the front...everyone is at least suffering from frostbite.' Obviously the situation here was different to a certain extent because the Sixth Army was surrounded by the Red Army, so medicine etc. for treatment of the wounded and ill was vastly insufficient - in Stalingrad, Antony Beevor writes how the shortage of plaster of paris meant German doctors had to bind shattered limbs with paper.

Another aspect of this is that while both sides would suffer greatly in the winter, even the Russians, the Russians always had men to replace those who died. The Germans, thousands of miles from home, did not have the manpower to replace their losses from attrition, the Russians had endless reserves. Colonel General Nikolai Lomov described how the number of men in the active army 'did not fall below six million people...deployed on the Soviet-German front from the Barents to the Black Sea' - so when the attacking side would come out of winter with severely depleted ranks, the Russians would always have more men to take their place.

The situation in Stalingrad was common all along the front, and indeed snowdrifts stopped the Wehrmacht within sight of Moscow in the winter of 1941, the coldest in a century. Private Albrecht Schimpf described how due to the lack of signposts they 'had to set the frozen bodies of horses along the snow roads to find the way during the snowdrifts.'

Another story, told by Major Hans Hinrichs goes as follows: 'We were attacked by a Soviet company in the early morning at approximately thirty-five degrees below zero. This company attacked was repulsed and the Soviet soldiers remained motionless about ten hours laying in the snow and in the evening they attacked again in the same spirit.' The Soviets were simply more used to the incredibly harsh conditions of the winter - no other nation that fought in the war, except the Finns, masters of winter warfare who the Russians learnt many lessons from during the winter war, would have been so capable of fighting in the winter. And that is why they have continuously repulsed attacks throughout the centuries. I'll end on one last recollection from Captain Ekkehard Maurer - 'The Russian soldier was a robust and hardy soldier, well used to those climatic conditions. Sometimes we got terribly angry because for instance we had to leave behind or drop our arms, machine guns or what have you because they didn't work any more [due to the cold], and the Russians just grabbed them, we saw sometimes, put some winter oil on them and used them against us.'

The Eastern front was insanely brutal during the second world war, resulting in a loss of life of over five million soldiers from the armies of Germany and her allies, plus 10 million Soviet soldiers and just as many, if not more, Soviet civilians. This is very well visualised by this video, which I highly recommend: http://www.fallen.io/ww2/

Sources:

Stalingrad - Antony Beevor

The World at War - Compilation of unaired interviews from the TV series - Richard Holmes

The Second World War - Antony Beevor

This website on page 4 is where I found the average temperature for Oktjabrsky Gorodok.

I would cite Stalin: The Court of the Red Tsar by Simon Sebag Montefiore but I haven't yet reached the section about the Second World War.

I hope this helped, and feel free to ask follow up questions which I will attempt to answer to the best of my ability.