I've always considered the phrase 'cold war' to cover from post ww2 (Truman Doctrine perhaps?) to 1991 when the soviet union collapsed. I'm readying a book (really just a collection of questions and essays) published in 1972 called The Cool War, in which the author Robert Imlay says the following about the Cuban Missile Crisis:
".... this point has to be established at the outset and with it a companion concept that the crisis marks the end of what is commonly called the Cold War".
He goes on to make that point that the threat from the USSR was still present in other ways, etc, so he isn't saying the conflict abated in any way, just that the period known as the 'Cold War' was over. Was this a common or even uncommon perception among people at the time?
This is a hotly debated issue among Cold War historians. Although it is common to cite the end of the Cold War as 1991, a few short years after the symbolic fall of the Berlin Wall, it depends more on what aspect of the Cold War you are looking at. The Cuban Missile crisis was probably the final direct showdown that the Soviets and Americans had and was a moment of intense tension and fear, but proxy wars across the globe to prevent the spread of Communism raged on and there were several confrontations during the period of détente as well (the Afghanistan proxy war and Prague Spring stand out in my mind). In my mind, the Cold War really started winding down when Mikhail Gorbachev became President of the Soviet Union as he peeled back the Communist roots with quite progressive domestic reforms that led to the gradual movement away from Communist powerhouse to a similar Russia we see today. Hope this helps!