I went through drills for "what to do in the event of nuclear bombardment" . It didn't bother me as much as it amused me.
In most schools, we would exit to the hallway and stand there. (Never however, opposite the door, as that was dangerous - the glass could hurt us!). And never in the top floor hallway.
The most absurd, had to be when I was in a 6th grade class and we were in a portable classroom. These things were apart from the main building. We exited, walked across to the main building, up a dozen steps, entered the building, up a few more steps, through a door, down a hallway, through another door and then down to the basement.
Even then, I realized it was ridiculous. We would have been dead before we even got to the main building.
Nothing about any of the nuclear weapons stuff scared me. I don't know if anyone else thought this way.