Hitler might, might have captured Moscow but it is doubtful. If you look at the original 1941 campaign closely AGC was close to failure militarily just on losses of manpower and equipment as it approached Moscow. The Germans really needed to stop and regroup and restore their units fighting strength. The Soviets had the depth of reserves available and moving to the front to make a stand before Moscow particularly given the low strength of AGC.
The weather would have made no difference.