If the Cold War escalated, it would have been a nuclear war. The world was still pretty fresh off of WW2 and the last thing they needed were to giant nations throwing nuclear bombs across the world. Instead of the two superpowers fighting a nuclear war, they instead fought loads of mini proxy wars. Examples of these are the Angolan Civil war, Korean War and the Vietnam war. Sometimes they did get directly involved but that was rare. In short, the Cold War was not a conventional one, but a silent one that occurred across the world where two superpowers expanded their influence until one collapsed.