The Cold War was a war of words more than fighting with actual weapons, but the psychological effect in Europe was stunning. Germans went from exterminating Jews & different groups to being given Hershey bars by African-American GIs, all because of their exposure to American culture. Was one of the main negative effects of the Cold War that it created a culture of fear and conformity around the world?
I think that you are right in that a good case can be made that the culture of the Cold War of conformity and constant suspicion was exported across the world. Nations around the world had to fight the reality that they would become satellites or proxy destinations for the Cold War. All over the world, nations understood that at any given time and if the conditions were right, they could be subject to the Cold War tensions. Nations like North Vietnam who were fighting for freedom and independence found themselves inserted into the middle of the Cold War fray between Western democracy and Soviet and Chinese style Communism.
The Cold War created an air of binary opposition, where one was either "for" or "against." Being able to explore nuanced notions of cultural identity as well as the condition of being in the modern setting could not be permitted in the Cold War mentality. Both the Soviet Union and America sought to increase as much influence around the world and, in doing so, exported the Cold War perception of consciousness around the world. The same paranoia that infected both nations was seen around the world in a lack of trust, reliance on military means to solve problems, and the idea that geopolitical reality was seen in terms such as "win" and "loss." It is in this light where the Cold War was worldwide in the attitudes and perceptions across the world.