Fortunately in the event of a nuclear winter you only have to follow this travel advice
Since all of the world’s nuclear powers are in the northern
hemisphere, stay south of the equator.
Countries like Australia, New Zealand, South Africa and Argentina are
temperate with plenty of space to grow food, and since they’re well
out of the way you’re unlikely to be targeted.
If you choose to stay at home, it’s probably best to avoid Alice
Springs, due to America’s top secret facility at Pine Gap.
According to the classic post-apocalyptic fiction On The Beach by
Nevil Shute, Melbourne is an excellent bet. The plot suggests that if
nuclear war breaks out in the northern hemisphere, the Victorian
capital is likely to be one of the last places the radiation cloud
If war spreads, you could always go further south to Antarctica. It
will be chilly, but with adequate supplies and shelter you could
survive several months.
This suggests that the more likely survivor countries will be Argentina, Australia, New Zealand and South Africa.
However, all is not lost for the survivors in the Northern Hemisphere. This scenario about a global nuclear war between the NATO and Warsaw Pact nations and occurring in 1988.
It estimates ~3 billion survivors a year after the exchange, and ~45 million survivors in the US alone.
The geopolitical situation has moved on significantly since this scenario was devised. So the re-establishment of a GMD Nationalist government in China is a fantasy (it would take an interesting set of political conditions for this to happen). The glib statement about peat bogs burning for several years overlooks the fact that this will contribute substantially to global warming in the post-WW III world.
This scenario can be used for guidance. It suggests that the US government is most likely to survive. While, by 2040, or fifty-two years after a nuclear war in 1988:
Some of the surviving nations have emerged by now as major powers, including Australia, New Zealand, China, Argentina, and Brazil.
Obvious the place to be in the aftermath of a nuclear war and in the event of a nuclear winter is to go South.
The question was about which Third World countries will survive in the event of a nuclear winter. Australia and New Zealand are certainly First World countries. Argentina and Brazil can almost qualify too. China historically has been a major super-power, and is modernizing fast but may fit the bill of being a Third World country. South Africa has a mixture of affluence and poverty. All in all, it is more probable that many nations will survive with their governments intact. Most likely they will be coalition governments or military dictatorships but generally similar to the governments during the Firs and Second World wars. Third World nations are probably going to be "eaten up" by stronger nations in their rush to survive and rebuild.
A recent review of the consequences of nuclear war specifically about the climatic impact. While the Physicians for Social Responsibility published a report suggesting even a limited nuclear war will result in global climate change and a famine affecting two billion people.
Research was unable to find anything about the impact of a nuclear winter on the South East Asia region. Nations like Malaysia and Indonesia surely will survive. While countries close to China will politically realign themselves in its sphere of influence to ensure their survival. Possibly India and Pakistan will wage nuclear war against each other, but if the northern hemisphere has been devastated this might stay their hand.