Cuba in the Cold War By tlstanley Period: Jan 1, 1950 to Dec 31, 1970 Cuba in the Cold War Apr 1, 1960 Bay of Pigs Invasion 1500 Cuban exiles waded ashore in Cuba. 1200 of them were captured and the rest were killed. Castro remained in power. Apr 6, 1961 JFK & FC John F. Kennedy and Fidel Castro