Rather depends which government.
There was massive propaganda on both sides. The US and others spread lies. The Soviets prevented anybody from telling the truth.
As Orwell predicted it was useful to maintain the fiction of an enemy it justifies all sorts of actions and secrecy that otherwise is difficult and phenomenal spending that would not be tolerated. (That the Snowdon revelations come as something of a shock to so many suggests a breathtaking naivety). When things go wrong you have someone to blame. Wonder why Korea gets such bad press, nowadays?
Anything was fair game – showing off at the Olympics to the race for space, from a nuclear arsenal that could never be used to feteing everyone in the arts who defected from one side to the other – spending zillions of dollars and roubles until the first one ran out of cash. Proof if such were needed that you can fool all of the people some of the time (and some of the people all of the time)
The irony was that it was pretty much unnecessary as the communist ‘experiment’ was failing of its own flawed ideology without much help from the West, in the meantime an awful lot of people came to grief in pointless wars in Asia.
During the Cold War, Americas Government tried to distance itself from Communism and shape the public opinion by adding the line; “in god we trust” to the currency and adding God Into the Oath. Basically an attempt to make the nation more Christian, which is intact false as America is a free multi theistic nation (meaning multiple religions) and allows all people of creeds and nations to live here.
They also showed propaganda posters of American troops burning with a title of: is this tommorow? And movies like “I married a communist” and “Red nightmare”. even Comic Book super heros like Superman started fighting Russian Badies. All in attempts to demonise communism and the Russians.
Take a look at video games today, even still we show the bad guy often being a Russian in games like Call of Duty and Battlefield 3, and now as the North Koreans are becoming a threat games like Home front have started demonising them to.