Which countries were in conflict during the Cold War?

The Cold War started as an ideological 'war' of threats and posturing. The primary countries did not fight with each other directly -- they made threats and tried to bully. Those involved were The Allies (USA, England, France, possibly Canada) vs. The Soviet Union (Russia). Russia supplied Cuba with missiles, which was too close for USA comfort.

The Cold War was primarily between the United States and the USSR/Russia. It was about the arms race, a race of secrecy to acquire the best, most powerful weapons the quickest. The USA knew the power of nuclear weapons, since the US dropped the H-bomb on Japan. President John F. Kennedy tried to get Russia and Cuba to see the error of their ways. But there were no diplomatic avenues; the Powers weren't negotiating very well. The Arms race meant everything to Russia, but the US viewed nuclear weapons as a last resort threat to the entire human race and to planet Earth.

As it continued, The Cold War consisted of various proxy wars fought over a period of several decades from 1947 to 1991. The primary coalitions during this time included the capitalist members of NATO aligned with the United States and the communist states of the Warsaw Pact aligned with the Union of Soviet Socialist Republics (USSR).

The Cold War proceeded and as proxy wars included the Korean War, the Vietnam War, and the Soviet War in Afghanistan, as the Powers did not directly engage each other (knowing it would cause World War III), but they engaged other countries in warring. Combatants of the Korean War include South Korea, the United States, the United Kingdom, Australia, and Canada versus North Korea, the People's Republic of China (Red China), and the Soviet Union. Participants of the Vietnam War include South Vietnam, the United States, South Korea, Australia, and the Republic of China (Taiwan) versus North Vietnam, the People's Republic of China, and the Soviet Union. Finally, the Soviet War in Afghanistan was fought between Soviet forces and the Afghan Mujahideen.