It depends on what you consider the "cold war" to be.
In terms of a threat to American sovereignty, it was a bunch of bullshyt (though Red Dawn is still an all-time kick-ass propaganda movie)
In terms of a threat to American hegemony, it was very real. From Africa to Central America to Southeast Asia to South Asia to the Middle East, governments everywhere were trying to escape American/corporate control and run their own nations for the best benefit to their own people. That conflicted with American access to resources and corporate profits. We had to shut down the African socialists so we could maintain access to their mines, we had to shut down the Middle East oil nationalizers so our oil barons could extract their oil for ourselves, we had to shut down the Central American land distributors so our corporate farmers could keep the bananas and beef flowing, we had to shut down the Southeast Asian independence movements so our clothing and toy factories could continue to bank off cheap labor without interference. And USSR, however bullshyt they themselves were when it came to national sovereignty, was still the nation primarily funding and aiding small countries who tried to stand up to the USA. In that sense the Cold War was very real.