like Hitler attacked his neighbors, Rush in take the capital and the rest of France, Austria, Holland etc will fall

There were many things that led to the defeat of the Germans and it started before Barbarossa even got started with the Yugoslavs providing a much greater fight than the Germans expected and thus holding up a great deal of manpower until they had the Balkans secure.  Getting a later than expected start while waiting for the forces from the Balkans meant they had less time to take Moscow and Peter before winter would settle in.  Further, it was a late year for the spring thaw meaning transport was more difficult in the initial phases and the fall rains came early meaning more mud at that time.

In any event, yes, winter arrived a bit earlier and stronger that year but there were other events that fed the defeat that was fairly well set in motion within two months of the start of Barbarossa.

The Russians threw forces into the initial battles  and allowed attrition battles to wage in some places (e.g., Smolensk) in order to hold up foot soldiers of the Reich.  At the same time, they mobilized about twice as many ready reserves as the Germans thought the Soviets had overall and regrouped farther back with more modern air forces and artillery that hadn't been utilized in the beginning.

As the Germans continued to push, they overextended themselves.  When they finally had control of those insurrection zones farther back, the foot soldiers finally came forward but were constantly picked at by partisans.  In general, many of the border towns allowed German passage and welcomed their liberation from Stalin.

Before the foot soldiers could arrive at the front, the Soviets began to attack German forward lines, which were mostly light armored forces, with air and artillery.  This was not in friendly terrain for maximum mobility and air back up was difficult because they had few forward air bases suitable to handle the necessary aircraft (mostly partisan activity - in its initial stages at that point - prevented this but it was also the terrain itself and the lack of compacting equipment, joined by the scorched-earth policy of the Soviet organized forces in retreat).

By August, the Germans were severely stretched and they found partisan activity increase on their supply lines all throughout that year as more and more locals revolted against the Germans in light of the harsh tactics of SS forces...in severe contrast to the regular army troops.  These partisan attacks made the situation with the supply line and the stretched forces up front even worse.

Now, almost two months to the day after the start of Barbarossa, with the Southern Front moving a bit more slowly than they thought it would and the Northern Front slowed in approach to Peter by a severe and strong Soviet organized military resistance (basically throwing a bunch of bodies with guns at the Germans but, given the manpower on hand, not ineffective), Hitler decided that much of the air support and many foot soldiers should be supplied to the North and South to finish those areas off before the push to Moscow.

Since Soviet strength was concentrated in the Center, they were able to attack a weakened line until the Germans regrouped in muddy October to make the push for Moscow.  By then, the Germans were tired (foot soldiers by non-stop fighting) and more depleted (armored units in the center through constant attack while air and foot resources had been deployed north and south).

They made the push but it was too late.

So, to recap:

• late start in a later than average muddy season with reinforcements coming from already tired Balkan campaigners
• mixed tactics by the Soviets (not planned that way but effective) that forced supply lines to move forward more slowly than the battle
• double the mobilization of Soviets vs. German planning
• lack of foot and air support to forward lines and a difficulty with transporting available foot soldiers
• Hitler spreading out the German strength even more to support north and south operations
• early rains in the whole region meant more health problems for unprepared Germans and more supply line and mobility problems
• early winter, which was the final nail as the Germans were wholly unprepared for a battle that would go that long

Their industry was unprepared for a sustained campaign, their troops were already over-tired and over-stretched, they did not have adequate heating units for equipment or clothing for troops to ensure sustainability through winter, and the local populations turned against them, thanks to the SS, which meant even more morale loss among ordinary troops about to be stuck in frozen, lonely, vast plains across the Soviet Union.