Having been there in the 80s I seem to recall the fear was global cooling, and that we'd all be dead before the turn of the century. Glad they were wrong then. Hopefully, we're wrong now.
And it mostly worked.
The first time I was ever mad about politics was in grade school, when some fake magazine for kids (probably one of the ads from Scholastic) had an interview with Ronald Reagan, and what the interviewer thought kids needed to know about Reagan was how crazy he was for jelly beans.
If I had known the phrase, "What in the actual fuck?" I would have said it out loud.
It would be 6 more years before someone summed up how terrifying the 1980's were and that man's name was Phil Collins (Genesis, Land of Confusion). But those bases were already loaded with... well, take your pick. You can go with Michael Keaton Movies about the crumbling economy or West German rock bands with a sprinkling of Sting ('Russians') while we all collectively crossed our fingers that we wouldn't wake up on The Day After.
https://harpers.org/archive/1958/09/the-coming-ice-age/
I have a distinct memory of my “science” textbook in 2nd grade circa 1981 had a section on the upcoming ice age. Once I realized that the book was old enough to not include the moon landing I didn’t pay much attention to it.
In any case, the idea about an impending ice age was in the science zeitgeist, at least the layman understanding of it well before the 80s.
https://en.m.wikipedia.org/wiki/United_Nations_Framework_Con...
The only underlying science was some debate about whether air pollution, the kind you can see and scrape off your skin, was going to be so bad that it would offset the greenhouse effect. But Nixon effectively ended that debate with the Clean Air Act.
https://www.jstor.org/stable/1756074
I mentioned it in an earlier comment but it was also in my science textbook in my elementary school days.
The science it was based on, of course, was the fact that ice ages are cyclical and we are well towards what would typically be the end of an interglacial period:
"the last four interglacials lasted over ~20,000 years with the warmest portion being a relatively stable period of 10,000 to 15,000 years duration. This is consistent with what is seen in the Vostok ice core from Antarctica and several records of sea level high stands. These data suggest that an equally long duration should be inferred for the current interglacial period as well. Work in progress on Devils Hole data for the period 60,000 to 5,000 years ago indicates that current interglacial temperature conditions may have already persisted for 17,000 years."
-- https://www.usgs.gov/faqs/how-long-can-we-expect-present-int...
You also had the fact that some of the coldest (and snowiest) winters on record in the US were during the 1970's, most notably during 1977 when it snowed in Miami and the Bahamas for the only time in recorded history, and temperatures in much of the midwest stayed below freezing for over a month. So of course articles about a new ice age would attract readers, even though any return to ice age conditions would happen over centuries, if it wasn't disrupted by humans.
It really was a lot of snow though, we were out of school for like two weeks in the spring of 1978.
In the Fort Worth Star Telegram, 27 Sep 1981, is the article "World's mercury inching upward", discussing the science which wouldn't look out of place today. But it wasn't until the end of the 80s that the US government started to take it seriously.