This analysis works only if you believe it was the weather that stopped the Germans. I would disagree with that. It was the distance and the Soviets that stopped them. The force that made it near to Moscow was a completely spent force. Offensive operations even against a weakly defended Moscow was impossible. And Moscow was not weakly defended.
Had they started earlier they a) might have still faced the mud of the spring thaws, and B) the Soviet response of rebuilding their reserves, which was the biggest obstacle the Germans had, would also have started sooner.
The Germans would have failed regardless. In all their operations they still took 25% casualties (725,000) in '41, which is low in comparison to what they achieved, but it wasn't replaceable. The Russians were reinforcing their army to the tune of 500,000 a month with the millions (14 million at the start of Barbarossa) of men they had who had military experience.
I absolutely agree with you. Yet, I think the weather in combination played a significant role in combination with the overextended supply lines and depleted forces. The lack of winter-proof equipment such as locomotives made the situation even worse.
Once the Soviets started to move their industrial facilities east toward the Ural mountains, the Germans did not have a chance due to the vast distances.