I was told they taught kids to duck and cover on the offchance their bodies wouldn't vapourize and they would be identifiable.
The Wikipedia article seems to suggest it was reasonable advice (and under the circumstances, the best advice) derived from the experiences of Hiroshima and Nagasaki survivors.
But it was probably only applicable to Hiroshima-sized bombs, and not a great deal of use given how quickly hydrogen bombs, 100 times more powerful, were developed.
Also, it was during the pre-ICBM era, when the bombs would be delivered by bombers, probably to just a few urban centers and other high-value targets. More like a really nasty version of the London Blitz than what I and others grew up with toward the end, which was "when it's all over, half an hour later, the entire northern hemisphere will be glassed, flattened, and/or on fire, or in the fallout plume from something that is. then the endless winter sets in."
I do not miss the Cold War, no.