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The big problem for the Germans that you are ignoring robertmikael is the resistance. (It often forgotten in these threads.)
The Germans couldn't advance further than they did even with good weather. They never managed to advance in the south, since their units had been fighting fierce battles with incredibly stubborn Soviet resistance and now came upon a strongly defended city.
They managed to advance in the north, taking a bridgehead across the Moskva-Volga canal, they weren't driven back by cold but by fierce counterattacks.
Attacks directed from the immediate west was again pushed back by Soviet counteroffensives after the attacking Germans had been seriously weakened by heavy soviet defenses. Not to mention the very fierce fighting that had been going on already since September.
The logistics that AvNY points out makes sure the Germans never was able to replace the losses they took. The Rasputitsia slowed the German advances and made logistics harder but in the end they never were able to end Soviet resistance and recover the losses they took fighting towards Moscow.
For the Germans to be able to advance more quickly you need to solve the problem of being able to replace losses much quicker, especially in terms of armored vehicles, ammunition and fuel.
And in order to fix that problem you have to fix the problem of logistics. Even before the rasputitsia set in the logistical situation was very dire. The distances are simply too great and the losses are too heavy. And most importantly the resistance is constant and it is heavy, some suggest it just got worse the closer they got to Moscow.
Then of course we could discuss the notion that the Stalinist regime would ever sign any kind of peace treaty anyhow. I find it highly implausible. Such an agreement would just mean a complete destruction of the Communist experiment and the top brass not having much options but suicide. I doubt they would do that in Yaroslav, perhaps in Kamchatka.
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