During the Cuban Crisis when thermo nuclear war was probably just a button push away from happening a lot of people were planning to go to Ground Zero and get it over in a flash. Many thought it would be impossible to survive for long after a nuclear war had taken place.
If it had happened then the plans were that those civilians still alive after the attacks would have been put under strict military control and sent to "safe places". Only a few chosen ones would have been given medical care and food. Others, the injured and those with little value to the rebuilding of civilisation, would have to fend for themselves in "camps" where many would be allowed to die. It was seen as essential to ensure limited resources could be used to try and rebuild a civilised country.
Leaving the country to travel to a better place would have been prohibited even if it were possible.
Would those plans have worked, with hindsight probably not as those who were expected to leave their families and go into the nuclear proof shelters when the 4 minute sirens went off would not have left their families or would not have reached the shelters / bunkers before the blast doors were shut.