The nuclear peace theory is one of the recent explanations for the lack of major power war since WWII(conviently ignoring of course the Korean War and the Sino-Soviet Border Conflict). According to proponents of this theory, the reason the cold war did not go hot is because of the presence of nuclear weapons made war too risky. Now if you only had a simple view of the world that may seem like an easy explanation, but its not true.
First two quick facts:
1) The presence of more powerful weapons has never deterred war in history. See the invention of the machine gun and strategic bombing.
2) If MAD was the deterrant for the use of nuclear weapons, why has no nation used nuclear weapons on a nation that doesn't have it? A sense of fairness?
Now having put those hear are the real reasons the Cold War didn't go hot:
1) Neither side wanted it. The idea of world communism died with Trostky, from Stalin through Gorbachev the Soviets had no desire to fight for a world communist movement. Yes, they would support communist parties in order to increase their own power (all the communist groups they supported were Lennist and aligned with the USSR, they weren't too keen on supporting Maoists), but they had no desire to risk their power by starting a major war. And the US had rhetoric about supporting the cause of Capitalism and wnt to war to stop the spread of communism, but since Truman had a policy of containment not removal. In the end no war happened, because neither side really wanted to go to war with the other.
2) Americans believed the Soviets would win, the Soviets knew they would lose. What is interesting about the Cold War is that neither side believed it would win a hot war. NATO intelligence about the Soviets was lacking and because of various reasons NATO vastly overestimated the power of the Soviet Union. After the Cold War, NATO was suprised at how poor of a state the Soviet forces were and how many were paper divisions. The Soviets themselves knew they would lose a long hot war. They had an initial advantage, but they had fewer total forces than NATO, a smaller population, and a much weaker economy. The Soviets spent around 25% of their GDP on defense during the Cold War, while the US spent around 4-5% of its GDP and still had around the same amount of dollars spent. The Soviets knew in a long war NATO's advantages of economy and population would win. So the second reason the war didn't happen is that both sides thought they would lose and no one begins a war they think would lose.
3) Warsaw Pact unrest and American democracy. No president in the US wanted to be the one who started a shooting war, as they high casaulties would likely cause him to lose re-election and his part would lose seats in Congress. There is a reason it took so long to enter the World Wars. And in most of the Warsaw Pact the Communist governments were very unpopular. Much of the Warsaw Pact was kept in line through threat of the use of force. A war would move many of those forces out of the disloyal regions, and any loss would remove the veneer of Soviet Invincibility.