The "ice age" theory never had much support as I recall, and was more an artifact of the cesspool that is science journalism.
It was supported, and is still supported (an ice age is coming, the question is whether AGW will hit us first). If you look at the timeline, it was like this:
1950s: Drastic increase in number of weather stations, making it much easier to measure temperature. Scientists noticed temperature was dropping, might be entering an ice age. Some talk about AGW (for example, at the advanced institute), but it was generally considered not a problem.
1960s: Continued temperature droppage, not much interest in the topic, general awareness that if glaciers return, we might have to find a way to melt them. Ideas like putting mirrors in space to warm things up.
1970s: Temperature started leveling out and increasing, more scientific papers appeared about global warming. Ice age idea wasn't dropped, but AGW was attracting more interest.
The 'cesspool' was mainly centered this quote in Newsweek from the 70s, I think:
“The central fact is that, after three quarters of a century of extraordinarily mild conditions, the Earth seems to be cooling down. Meteorologists disagree about the cause and extent of the cooling trend, as well as over its specific impact on local weather conditions. But they are almost unanimous in the view that the trend will reduce agricultural productivity for the rest of the century.”