They said entire continents got swallowed whole, however. That's a global warming thing, right?

No it would be cooling. The debris would layer the Earth so less sunlight would get in, thus everything gets cooler. That is a pretty general term for nuclear winter, and it is unclear if there was a nuclear winter at all, as it wouldn't have lasted to Fallout 1.

I did not read that post sorry, I just write from what I know would would happen.

Nuclear weapons completely destroyed the Ozone Layer and the Sun's harmful rays would've killed off all life if nuclear winter hadn't set in. I guess the Ozone reformed after time but not to its original strength which is probably why it seems like everwhere is a desert.

It is true that even a limited nuclear exchange would likely destory the Ozone layer and wipe out all life on earth. [regardless of nuclear winter] but that research is much more modern. Fallout is based in 1950's science fiction and a desert wasteland is what they imagined as the outcome of Nuclear war.

I'm pretty sure they knew about the ozone layer and thought that it might be destroyed by nuclear weaponry, I'll look it up.

Andperhaps they believed that nuclear winter would block out the sun for long enough that they ozone layer could reform a bit before the dust clears.

EDIT/UPDATE- I looked it up, we discovered that the ozone layer existed in the late 1800s so they might've thought that it would be destroyed by nuclear weaponry, I don't know and nothing comes up when I Google it...

Massive global ozone loss predicted following regional nuclear conflict

We use a chemistry-climate model and new estimates of smoke produced by fires in contemporary cities to calculate the impact on stratospheric ozone of a regional nuclear war between developing nuclear states involving 100 Hiroshima-size bombs exploded in cities in the northern subtropics. We find column ozone losses in excess of 20% globally, 25–45% at midlatitudes, and 50–70% at northern high latitudes persisting for 5 years, with substantial losses continuing for 5 additional years. Column ozone amounts remain near or <220 Dobson units at all latitudes even after three years, constituting an extratropical “ozone hole.” The resulting increases in UV radiation could impact the biota significantly, including serious consequences for human health. The primary cause for the dramatic and persistent ozone depletion is heating of the stratosphere by smoke, which strongly absorbs solar radiation. The smoke-laden air rises to the upper stratosphere, where removal mechanisms are slow, so that much of the stratosphere is ultimately heated by the localized smoke injections. Higher stratospheric temperatures accelerate catalytic reaction cycles, particularly those of odd-nitrogen, which destroy ozone. In addition, the strong convection created by rising smoke plumes alters the stratospheric circulation, redistributing ozone and the sources of ozone-depleting gases, including N2O and chlorofluorocarbons. The ozone losses predicted here are significantly greater than previous “nuclear winter/UV spring” calculations, which did not adequately represent stratospheric plume rise. Our results point to previously unrecognized mechanisms for stratospheric ozone depletion.