A thought experiment if you will.

Imagine D-Day without the american beach heads. You still had Sword, Juno, and and Gold, just not Omaha and Utah.

Now lets say the Eisenhower was still in charge and lets say that they where using primarily American guns with American ships and American planes. Just not American Troops.

Would you say that D-Day was a peaceful day between Germany and the US?

Basically the cold war was in a lot of ways like that but on a global scale.

The US and the USSR may have not come to blows but they used Proxy battles to fight it out.

In a way the Cold War was very hot. It just hinges on how you view conflict between two nations.

The USSR funded and armed countries and the US funded and armed countries and they fought each other using subordinates. Sometimes it was so mixed up that for example Vietnam even saw Russians killed.