What problems did Western Europe face during the Cold War?

The Soviet Union, at the conclusion of World War II, had installed pro-soviet governments on its western border.  Winston Churchill was the first to use the term "Iron Curtain" to describe the division within Europe.  In 1956, Hungary was invaded by the Soviet Union after the students rioted and moved political leaders to withdraw from the Warsaw Pact.  The rebellion was quickly crushed, and served as an example to any other bordering country of what the cost of rebellion would be.

The US and allies, having "liberated" Western Europe, continued to maintain democratic governments and had established NATO.

What's interesting to note are the troop and materiel concentrations along the Iron Curtain.  The Soviets had several times the amount of conventional weapons (tanks, troops, planes, etc.) than the West.  Instead, all the countries on the western side had huge missile installations, armed with both nuclear and conventional warheads.  Strategically, this suggests that the Soviets, if given the chance, would move westward; it also suggests that the West would not move eastward, but would risk nuclear war to preserve Western Europe from Communist control.  So the region lived in fear of nuclear annihilation for most of the Cold War.