“Hitler lost his nerve during Barbarossa” In doing what?
Barbarossa failed because the Blitzkrieg failed… The initial plan (a little bit like Napoleon) was to destroy the Russian/Red army at the borders then to oblige the Tsar/1st Secretary to negotiate or capitulate.
In both case it didn’t work and the Russian armies did succeeded to retreat with heavy loses in both cases.
Then the German’s equipment was not designed for a long war of attrition (no strategic bombers, short range fighters, light and medium tanks with narrow caterpillars –good for French roads, not good for Russian plains and mud).
However, the first counter-offensive in Moscow is launch by Zhukov in end of 1941, so merely 6 months after the start of Barbarossa.
These are facts.
Putting the German defeat on winter is absurd. As one of them said if you can’t predict the weather you can predict the season, so to be surprise by winter is more that surprising…

“Had he given them free reign” Again, to do what? They did what they could, until they faced not only KV5 and T34 but generals able to manoeuvre them…

The panzers were useless in Stalingrad, Leningrad or Sebastopol. The Red Army succeeded in imposing their war to the Germans. No fast and daring manoeuvres, no, just fortified position and use of artillery and infantry you can’t ignored or avoid.

“All of Hitler's generals begged him not to do it”: So what the generals wanted to do? Kursk was a gamble. It looks like Hitler and Stalin had some secrets negotiation and Stalin wanted a return to the borders of 1941. Hitler decided to show he still had teeth…
Even a victory in Kursk wouldn’t have defeated the Red Army at this point…
Remember that the attack on Kursk was called off because the Russian started an offensive on other flank (and because the Russian defences were still holding)… It was the last cast of dices to regain the upper hand, the initiative.
Like most of the Hitler’s plans, it makes sense until you’ve got the realty check…But that was the idea…
Concerning Moscow, Stalingrad and other major failures, most of the time that wasn’t Hitler initial plan… It was his generals who convinced him to take Moscow, or Stalingrad (and later of couse blamed him for their own failures).
Hitler was more obsess by oil and ore (reason why he had to attack Greece when the Italians embarked in this war, The Italian defeat put the Rumanian oil fields within the English bombers range) than in symbols. At least at the start of the war…