The Cold War wasn't an physical war. It ws more of a sever extreme tension disagreement. Between the Soviet Union and the U.S. after World War II
The Cold War had started by 1947, when the U.S. aid provided the Marshall plan. Western Europe had brought those countries under american influence and the soviets had installed openly communist regimes in eastern Europe.
The U.S. and Great Britain feared the permanent soviets domination of eastern Europe. They feared the threat of Soviet Influenced communist parties coming to power.
The Soviet Union was determined to maintain control of eastern Europe in order to safeguard against any possible threat from Germany. There intention was to spread communism world wide.
The United States and its European Allies formed the North Atlantic Treaty Organization. A unified military command to resits the soviet presence in Europe.