I think if Hitler did win then the cold war most likely would still happen, except it would be between Germany and the US instead of the soviet union. After driving allied troops back to the west and invading Russia as He had originally planned. I could imagine the defeat of the Soviet Union to be particulary humiliating on their part, (Stalin and other Communist party leaders being brought to Berlin and paraded in chains.) However although He would have won WW2 His troubles wouldn't be over. There would most likely be constant insurgency within the east, surviving soviets would retreat into forests and mountains disrupting Nazi supply lines to and from Germany's newly found lebensraum. Germany would no-doubt be working on it's own nuclear weapons by the late 1940's, they were already experimenting with atomic energy during WW2 often studying the effects on concentration camp detainees. It would have only been a matter of time before they had atomic bombs of their own. Hitler during WW2 expressed a frequent desire of an attack on the US mainland, however He lacked the means to do so given that Germany's resources were already stretched towards the war in the east. I think eventually after a few years of peace between Germany and the US, and after a period of paranoia and perparation Hitler would eventually make the first move. Not sure if many people know this but Germany did actually send a small group of submarines to a New York harbor. They filmed the nightime city skyline through their periscopes, spooky eh?
With the death of Hitler however, the Nazi regime without it's charismatic leader would most likely crumble by itself. With the main aspect of its cult of personality gone, the regime would probably be torn apart by divison and infighting. With Hitlers death there would definately be a rise in the morale of guerillas and partisans leading to an uprising or two. The nazi reigme would probably start to become more moderate without being stuck to their values by their now absent fuhrer. A lot of Hitlers henchmen were both fanatical and ruthless but I doubt Goering or Himmler etc would have had the same charismatic effect on their followers. Slowly but steadily the regime would fall apart until an eventual collapse. Germany would then most likely begin to open peace talks with the US, (that is of course if Hitler is dead and He hasn't started WW3 by then.)