The embargo is not only about the Cold War. Cuba is one of the US’s closest neighbors and as a result has taken most of the refugees fleeing Cuba’s oppressive regime. This has made the Cuban-American lobby a big voice in politics, as many Cuban immigrants care deeply about what happens in their country of origin and to their families.
Cuba has remained hostile to America since the end of the Cold War. In 1996, Cuba shot down two civilian US planes. 
More recently, Cuba has jailed an American aid worker, sold arms to North Korea, and made deals with Venezuela. 
Cuba’s hostility towards the US has not been ended by the cold war. Cuba is of continuing importance to the Cuban-Americans, many of whom fled the Castro regime.