Some Cold War short stories revolve around the arms race. The constant building up of nuclear arsenals by both the US and the Soviet Union was a major part of the Cold War. There were stories of scientists involved in the development of these weapons, some with moral dilemmas, and also the political posturing of the leaders who brandished their nuclear capabilities as a form of deterrence.
One interesting Cold War short story could be about the Berlin Airlift. It was a time when the Western Allies supplied West Berlin by air to counter the Soviet blockade. This showed the determination of the West not to let Berlin fall. Another could be stories of spies during the Cold War, like the real - life cases of double agents who were constantly playing a dangerous game between the two superpowers.