I recommend to you the article Charles Sharp and I wrote for The Journal of Slavic Military Studies, entitled "Was it the Mud?" Our conclusion - no. Mud was a factor. It looms large in German memoirs, and German documents of the period. But only by guiding on the former and failing to carefully read the latter can you believe that the German offensive was stopped by the mud. There were other factors that were far more important.
1) The Red Army. After losing a million men in two weeks, it would seem there was nothing what was left of the Red Army could do to prevent a German waltz into Moscow. But it managed. Partly because of the lack of roads and their condition the Germans were only able to bring a portion of their strength to bear, and the Soviets matched them, if not in numbers, on every axis they tried to advance on. The critical clue - examine the German loss numbers in the last three weeks in October. And examine the condition of German divisions at the end of October, compared to the beginning of Typhoon. All those guys, and tanks, etc, did not die or get knocked out by being choked by mud. Someone was shooting holes in them. Wanna guess whom?
2) The roads. There weren't very many. For German purposes west of Moscow there were two, or three if you count the Old Post Road that ran parallel to the Moscow Highway. The other one was the Roslavl-Podolsk road. Over these the Germans attempted to supply two armies and two panzer groups. Wanna guess how that worked out? It caused enormous traffic jams for one thing. For another, it destroyed the roads, none of which were built to carry hundreds of tanks, tractors, heavily loaded trucks, guns, etc. As to the dirt roads, designed for peasant carts, sending one panzer regiment out to follow one meant after they had passed, there was no road at all. Their fuel trucks, schutzen, artillery, ammo, bread... had a hard time following. The Red Army again played a roll. Though they ran up a terrible record in 1941 for blowing major bridges, they did just fine on the small ones, and every culvert that ran under a road too. Putting 1,000 kgs of TNT under a road with a three day delay fuse can be a real drag too if you're trying to use the road. There are lots and lots of rivers and marshes west of Moscow. Everywhere a road crossed one, you had a low point. Blow the bridge and the vehicles will try to ford. Send enough heavy vehicles over this way and you have one magnificent mud wallow.
3) The logistics. As Halder put it, even after the war in an interview, "The material must be the servant of the spiritual; this means the problems of the quartermaster corps may never interfere with the operational plan." It could be engraved on the tombstone of the Wehrmacht. Fact - at the beginning of Typhoon, there was enough fuel to reach Vyazma. No more. It had been impossible to stockpile. More to the point, during the battle (I have the supply records of 4th Army), most days the amount they received from the Reich was... zero. On one or two days they got fuel delivered to the dumps around Roslavl. True, pushing it forwards, through the traffic jams, was no joy and could take a week. But the bottom line was there was little or no fuel to push forwards. Food and ammo were also very tight (ammo less than food). In some cases, threadbare panzer divisions screaming for infantry relief had to demur when offered reinforcements. I've come across at least two instances when the infantry were warned not to come forwards, because it was impossible to feed the troops already at the front. Many divisions complained of no bread for a week...
The problem was the Red Army was supposed to collapse, as it was supposed to have done on the frontier. But it didn't. By the middle of the 3rd week in October, only 3 days after the Vyazma Pocket was declared liquidated, the Red Army launched a 3-army counterstroke that chewed up XXXXI Motorized Corps and left it hors de combat. Zhukov landed another counterstroke, albeit a weak one, in the fourth week of October on both the Moscow Highway and the Roslavl-Podolsk road that smashed four German infantry divisions and a panzer division, cut off 10th PzD on its drive north to Skirmanovo.
Someone above asked how Rotmistrov made his run to Torzhok. Simple. He had one tank brigade, with augmented repair assets, and was driving down a paved road (one of few). So he really made time.
Finally, on 1 Nov, Zhukov submitted a report to the Stavka. In it he detailed the German's condition, identified most of the enemy divisions facing him, and declared that the enemy would not be able to resume operations for two weeks, during which time he would have to bring up supplies, rebuild and reorganize some of his shattered formations, and bring up reinforcements. He got the time correct to the day. But what is interesting is what he did not mention. Every German memoir and KTB talks of how they need to wait for the Frost (always capitalized), if only the Frost would come, then, on to Moscow!! (It behooves one to be thoughtful in what you ask for.) At times Soviet reports speak of how nearly impassable the dirt roads were to motorized traffic (this after 19th Oct, when the rain began for serious and things did indeed get muddy.) But Zhukov makes no mention whatsoever about the weather, nor does he assign it any significance in determining when the Germans would resume. He identifies their problem as having a shattered spearhead, and being out of supplies.
German memoirs, and official reports, tend to be heavy on the excuses, all of which are attributable to factors over which they had no control. They successfully threw mud in they eyes of history. But if anyone had bothered to read their actual records, they would find all the material I cite above about roads collapsing under the weight of the German columns, the lack of roads, the lack of supplies, the traffic and lack of traffic discipline, the numerous blown bridges and their effects, , the fierce resistance of the Red Army and the horrendous casualties they had taken. Its all there, along with the daily weather and road condition reports. Pity most historians never really looked, since they already KNEW THE TRUTH!! It was the MUD!! It must have been.... but it wasn't...