As mentioned, the threat of Mutual Assured Destruction was enough to forestall the possibility of outright war; although one side or the other would have prevailed, depending on who fired their nuclear missiles first and who had the best anti-missile defense, there would have been massive radioactive fallout and probably retaliation as well as military reaction from other countries. Another factor was the increasing diplomatic relationship between the Soviet Union and the United States, which would define the political landscape for over fifty years.
The Berlin Blockade (1948-1949) was the first major conflict between the two superpowers after World War II; the USSR attempted to keep all support out of Berlin, to prevent help coming in from the Allies and by controlling supply, control the city. In response, the U.S. began airlifting supplies in and eventually were delivering more by plane than by train or truck, and the USSR had to remove their blockade in defeat. Because of the uneasy truce shared by the USSR and the U.S., the Soviets did not directly attack any of the airlifts, but instead used propaganda and harassment tactics to make delivery difficult. Despite air crashes and deaths, the airlifts were a success, and the USSR was forced to admit defeat and rescind the blockade. Again, direct military conflict would have been interpreted as a declaration of war by the U.S., and at the time it was not politically or militarily feasible.
Another factor, not expressly identified, is the increase in spying and espionage between the two nations. Despite political rhetoric, it would have been more beneficial to all parties for a covert, generally peaceful takeover, rather than a shooting war with many casualties, and this could have been achieved through covert operations, which would have been jeopardized by direct military action.
The most likely reason for this was that the two sides were afraid of the outcome if they were to fight one another. This was especially the case after both sides had huge arsenals of nuclear weapon and faced "mutually assured destruction" if they were to fight.
During the entire Cold War, the consequences of direct fighting between the US and Soviet Union were too high for either side to want to take on. For example, at the time of the Berlin blockade, the USSR would have had to worry about US atomic bombs while the US would have had to worry about the huge Russian army that could have invaded Western Europe. Later on, the calculus was much simpler since both sides had many nuclear weapons. This is most likely what prevented direct fighting at times like the Cuban Missile Crisis or the Vietnam War.
The Cold War was an entirely different kind of war than previous wars. Both sides, the United States and the Soviet Union were aware of the implications and the consequences if they used their military strength. Neither side wanted to totally annihilate each other but wanted to assert their power.
Thus, the Cold War became a war of words. Growing up during this time period I remember Premier Nitika Kruschchev on the television telling us that he would bury us. We had air raid drills and went into secure locations inside our school. May Day in Russia was shown as one of military strength as misslies were paraded in Red Square.
The United States through the strength and power of President Kennedy won the battle of words and the Russians removed their missles from Cuba. We came very close to World World III. This Cold War opened a new phase in diplomatic history during which those individuals in power realized that wars could be fought through discussion and not with weapons.
This philosophy was evident in Reagan's terms of office when he built his "star wars" defense system.