You probably mean "cold war" related wars. The way you've worded this question it could mean "any war", in which case there were probably hundreds of little wars fought on earth from 1945 to 1990. To include:
1. Wars in Africa against White rule (wars against Apartheid).
2. Wars in the Middle East (Southwest Asia) between the Israelis and Arabs.
3. Wars of power struggles else where on the globe; to include insurgencies.
There were some communist related cold war battles fought in Greece, Turkey, Central and South America, etc. But the only "big" battles were the two wars fought in Korea and Vietnam that directly related to communism vs the free world.
so what were the major battles of the cold war and why
Hot "battle" of the cold war. A war is a series of battles.
Korea and Vietnam were the only HOT Battles of the cold war; a war between the communist world and the free world.
No battles . I think you are missing the point of the Cold War because there were no battles it was called "Cold". There were a few standoffs and threats, but for the most part it was the western powers looking at the communist dictatorship through the lens of containment.
John Paul Jones
None, the cold war wasn't a war. However...Korea & Vietnam can be considered two "battles" of the cold war; since Korea/VN were "hot" (shooting & killing) wars during the cold war. The cold war was about communism vs free world. Korea/VN were both fought between communists and the free world.
The cold war was cold because there were no battles, therefore no one was killed in combat.
Battles were conducted in all of the Spanish New World Colonies.
John Paul Jones
As one of two hot battles of the cold war.
The Korean War (1950-1953) & The Vietnam War (1961-1975) were "Hot" battles of the "Cold War."
Cold War means NO FIGHTING. There was no war during the cold war, with the exceptions of the two "HOT BATTLES" of the cold war, the Korean War and Vietnam War. Actual war between the the USSR & the US never happened.