Who were the leaders during the Cold War period in Nicaragua?
The answer by pohnpei397 gets the names right but is misleading with respect to U.S.-Nicaraguan relations, both during and after the revolution that brought to power the Marxist-Leninist Sandinista regime. While the question was specific to the identities of Nicaragua's leaders, the answer included the comment regarding U.S. opposition to the Sandinista regime that is wrong.
The United States did not oppose the revolution that toppled the Somoza dynasty. Under then-President Jimmy Carter, the U.S. was actually sympathetic to the revolutionary movement, as Somoza did run a brutal, corrupt dictatorship. The reason the United States grew hostile to the newly-established junta run by Daniel Ortego and his brother Humberto, Tomas Borge Martinez, and Eden Pastora was the same reason the latter of those individuals, Pastora, broke from the Sandinistas: The Sandinista National Liberation Front was not socialist. The United States would not have opposed if it was merely socialist. Rather, it was Marxist in its orientation and, as soon as it took power, aligned itself with other regimes hostile to the democracies of "the West." The Ortegas, Borge and others were fundamentally opposed to the United States and immediately upon taking power began supporting terrorist and guerrilla movements throughout the hemisphere in coordination with the Cuban regime led by Fidel and Raul Castro. Sandinista support for terrorist movements in Peru, Colombia and elsewhere, and the fact that it imposed a more draconian dictatorship on the Nicaraguan people than the regime it replaced, that of Anastasio Somoza Debayle, were the reasons the United States opposed it. In fact, it was the Cuban and Nicaraguan regimes' alliance with the Marxist movement in Grenada, and their use of that tiny island as a logistical base for support of terrorist activities in Central and South America, that resulted in the U.S. invasion of Grenada on October 25, 1983.
On September 17, 1980, the Sandinistas assassinated former President Somoza while he was living in exile in Paraguay. That was symbolic of the nature of the Sandinista regime, not its economic orientation.
For the purposes of this answer, I will define the Cold War as the period that began immediately after the end of the Second World War and that ended with the dissolution of the Soviet Union in 1991. There are other ways to define it, but this is the one I will use.
For most of this time period, the most important people in Nicaraguan politics were the Somoza family. Three members of the family held the office of the presidency for thirty of the forty-three years that began in 1936. Even when other people held the office, it was the Somozas who controlled the country because they controlled the military. The three members of the family to hold the presidency were Antonio Somoza Garcia and his two sons, Luis and Antonio Somoza Debayle. If you need a list of the other people who held the presidency but were essentially puppets, follow this link.
In 1978, the country essentially experienced a civil war that ended when Antonio Somoza Debayle fled the country in July of 1979. This ended Somoza family rule. From then until 1985, the country was led by a junta which was “coordinated” by Daniel Ortega. This means that Ortega was essentially in control. He officially became president in 1985 and was in office until 1990. Ortega’s political party/movement was called the Sandinista National Liberation Front and was a socialist movement. This is why the US was so strongly opposed to Ortega.
In 1990, Ortega lost an election to Violeta Chamorro, who became the last leader of Nicaragua during the Cold War period.