Alot of people now a days see the Cuban Missile crisis as one of(or maybe the most) dangerous incident(s) of the Cold War, but to which extent was it viewed that way by politicians involved at both sides at the time of the crisis?
Both Kennedy and Khrushchev were fully aware that a misstep could set off a nuclear war. More than this, many U.S. generals were openly advocating immediate airstrikes on Cuba, followed if necessary by a full nuclear attack on the USSR. On the Communist side, Fidel Castro pushed Khrushchev for control over the Soviet nukes in Cuba and a preemptive strike on the United States.
This is not as insane as it sounds at first glance. The U.S. generals pushing for a nuclear strike on the Soviet Union had a decent idea of the strategic situation. They knew that the Soviets were catching up to the US in missile technology, and that soon any nuclear war would result in mutually assured destruction. The window of time where the United States could "win" a nuclear exchange, losing only a handful of cities, was closing.
As for Castro, he had faced years of CIA-backed destabilization, paramilitary invasion, terrorism, and attempted assassination. He had every reason to expect the Americans to invade Cuba. He further expected that any meaningful resistance would draw a nuclear response. His message to Khrushchev was basically: "In a week, we'll all be dead. We can't let the Americans kill 100 million people and just get away with it."
The Armageddon Letters came out a few years ago and seeks to examine this exact same question. The authors try to look at the conflict through the eyes and experiences of JFK, Khrushchev, and - especially - Castro.