take a look here : http://science.howstuffworks.com/nuclear-winter2.htm
The article details six levels of nuclear winter: Minimal, Marginal, Nominal, Substantial, Severe and Extreme (in the final case everybody and everything dies). For most of these scenarios; the conclusion from their analysis is based on this fact:
Everything below the equator would remain mostly unaffected, given the hemispheric separation of air currents and the fact that most nuclear targets exist in the Northern Hemisphere.
The worst level for which humanity will likely survive is this:
Substantial nuclear winter: This scenario, following full-scale nuclear war, involves catastrophic consequences for the Northern Hemisphere: freezing temperatures, widespread fallout, pollution, ozone depletion and disrupted precipitation. Imagine a deeply overcast day -- now imagine those conditions persisting for years. Green plants would barely receive enough sunlight for photosynthesis. Crops would fail, billions of humans would die, species would go extinct and while humanity would likely survive, civilization as we know it might not. Damage to the Southern Hemisphere would depend on the number of detonations below the equator.
In other words, the most plausible outcome for full-scale nuclear war is a hellscape in the Northern Hemisphere (where nearly all the major cities are) and a lightly damaged Southern Hemisphere (South America, Australia, the southern third of Africa, New Zealand, many islands).
If the Southern Hemisphere does suffer Nuclear Winter, it would be one of the earlier levels: Marginal would be plausible. You can look at those to see how much damage would likely occur in South America (or the southern hemisphere in general). Perhaps any big cities or major population centers would be bombed in a full scale war (thousands of nuclear bombs).
I live in Argentina and I think all here in South America would have to accommodate many people, basically anybody that survived in the Northern Hemisphere. The current population is around 420 million, perhaps tens of millions more would be refugees. This could trigger revolutions and new political orders and alignments, which may or may not be good.