I mean the operative word in "Cold War" is Cold. There was a lot of arms buildup and posturing, and some proxy wars in smaller or less developed countries, but no wars waged directly between the great powers. The Cold War was part of the long peace that HST predicted. I think you could argue that America's supremacy was never seriously contested by the USSR - sure the USSR had nukes, but the US had plenty of those as well, it had the better economy, overwhelmingly better navy etc. There were more chips on the strategic board than MAD and most of them belonged to the US.