The Cold War was fought predominantly between the Soviet Union (Russia today) and America. It was called the Cold War because not a single shot was fired. The Cold War was basically a pissing contest between the United States and Russia. Russia sent the first man to space, but America sent the first man to the moon. . . The Cold War basically changed our educational system by incorporating a lot different subjects, such as math and sciences, in order to compete against the S.S.R. A lot of other changes happened because the Cold War including in technology.
But, like someone else has mentioned, people did die. In fact, A LOT of people died. The USSR an expensive sword used for combat but had a dull edge. They looked very powerful from the outside, but were a complete disaster in general. NATO and The War Saw Pack separated the country into four equal parts. The East went to Russia, and the West went to America; Thus, the American side was Capitalist, while the USSR side was communist. The USSR side had serious problems sustaining governance: starvation, famine, homelessness, etc. While the Capitalist side fared better.
Communism, like anyone with a major in cosmetics, to any sane person, has never truly worked. Greed, lack of funding, and other factors make it impossible for Communism to function. The leaders were getting rich, while poor were starving to death. The basic principle of communism is that everyone makes the same amount, and through government assistance, the wealth gets redistributed. But this was never truly implemented correctly. Plus, let us not forget that no doctor wants to be paid the same as a factory worker and so on.
Because of these social economic problems, the people on the East side of the country did everything to get over the wall that was heavily guarded by USSR soldiers. People were shot and killed for trying to escape. There is actually a famous picture that I can not remember of a dying person lying in the snow afer sustaining a gun shot from a guard. The guard just sat there and watched him die without helping—a grave reminder to those who tried escaping. People drove cars into the wall.
So no wars were fought, but people did die. I guess that's not what you asked. He.