Paul W. answered • 04/15/19
Dedicated to Achieving Student Success in History, Government, Culture
Your question actually breaks down into two separate questions. (1) Why were the battles of the Cold War fought at locations all around the globe and (2) why wasn't the 'front-line' of the Cold War where the territories of the United States and the Soviet Union were in closest proximity?
I'll start with the question 'Why wasn't Siberia and Alaska the primary front-line of the Cold War?' With all due respect to Siberia and Alaska, neither of them contain the centers of population or industry of the nations that own these territories. If, for instance, Soviet forces happened to land in Alaska, they would have a long way to go to get to Washington, D.C. or anywhere else in the continental U.S. The same would be true for any U.S. forces invading Russia's Pacific coast; it's a long way to Moscow.
The shortest distance for land based I.C.B.M.s between the continental U.S. and the heart of the Soviet Union - Russia west of the Ural Mountains - was due north, over the North Pole. Of course, the opposite was true for Soviet land based I.C.B.M.s (this doesn't mean, however, that there weren't targets in either Siberia or Alaska at which U.S. and Soviet missiles were aimed).
When it was discovered that the Soviet Union had begun installing nuclear armed missiles in Cuba, it was seen as a dire threat because missiles based in Cuba would be a relatively short distance from the major population centers of the U.S. east coast - certainly far closer than the I.C.B.M.s based in the U.S.S.R. This meant that the retaliatory forces (our missiles and bombers) would have far less time to respond if missiles were launched from Cuba.
Of course, neither the leaders of the U.S. nor the leaders of the U.S.S.R. wanted the Cold War to become a Hot War, that is, an actual military struggle between their respective countries, knowing that it would inevitably escalate into nuclear exchanges that would make both countries, along with humanity as a whole, the losers in such a conflict.
Nevertheless, both the U.S. and the U.S.S.R. were determined to increase their influence throughout the world in order to strengthen their positions. This meant taking action - ranging from diplomacy to military intervention, and everything in between. The U.S. worked to prevent friendly countries from changing sides and joining the Soviets, to convince countries that hadn't yet taken sides in the Cold War to join with the U.S., and to do what it could to turn countries friendly to the U.S.S.R. in to allies of the U.S. Of course, the Soviets pursued the same goals in their favor.
This meant that the opposing sides faced off against each other in Europe, the Western Allies of World War II forming the North Atlantic Treaty Organization (N.A.T.O.), while the Soviet Union organized their puppet governments in the countries of Eastern Europe into the Warsaw Pact military alliance.
In the developing world, the nations of Africa, Asia, Latin America, and the Middle East (many of them newly independent former colonies of European nations) were encouraged to take sides in the Cold War. Conflict in the developing world served as proxy wars between the U.S. and U.S.S.R. (the Arab-Israeli Wars, for instance) or resulted in the direct military involvement of one side (the U.S. in Korea, the Soviets in Afghanistan). Involvement in the conflicts in the developing world stopped short of transforming the Cold War into a Hot War - into combat between the armed forces of the U.S. and U.S.S.R. - and so it was pursued by both sides as part of their efforts to expand their influence.
