a lot of people say that, but given that most likely no Nukes would be used in Africa, or Latin America, maybe even Oceania, i don't see how the Human race would die out.
The species would survive, after a fashion.
One of the great myths of the Cold War was "the Southern Hemisphere is safe". It wasn't. It was less filled with targets, but it was far from safe.
A short target list
circa 1985:
South of the Equator
Rio de Janeiro, San Paulo, Montevideo, Stanley, Cape Town, Johannesburg, Diego Garcia, Jakarta, Perth, Melborne, Canberra, Sydney, Brisbane, Auckland
South of the Tropic of Cancer
Havana, Guantanamo, Balboa (Panama), San Jose,
Managua, Kingston, San Juan, Caracas, Dakar, Lagos,
Mogadishu, Djibouti, Mubai, Karachi,
Ho Chi Minh City, Da Nang, Cam Ranh Bay, Hanoi, Singapore, Brunei, Hong Kong, Manila, Cavite City, Taiwan, Guam, Oahu, Lahani, Hilo
Additional African Continetal targets
Tripoli, Cario, Rabat, Algiers, Tunis, Alexandria
This list, of course omits the various oil ports in the Persian Gulf, Arabian Peninsula, Nigeria, & South America; other targets in Pakistan, India, South Africa, Asia, various port's of call that may have a British, U.S. or Soviet vessel present when the ballon went up.
The list is arrived at by looking at American or Soviet bases, probable "safe harbors" for one fleet or another, sources of strategic supplies, and other vital resources. The targets in
bold are American, the rest are Soviet or local (e.g. India/Pakistan).
It is also important to note that, in the case of a full exchange, the likelyhood of biological weapon release, either intentional or accidental, is exceptionally high. These weapons are, without question, the most dangerous element of any full exchange as their actual lethality and spread in the wild is impossible to accurately predict (this is especially true in the case of "engineered" viruses, a subject of intensive Soviet R&D). The virtual depopulation of the Americas (North & South) & Eurasia is a distinct possibility, with a reasonable chance of serious losses in North Africa.
Lastly, it is critical to recall the overwhelming dependency of African (and, for that matter all large) cities on food imported from the Americas and Australia. Without a solid infrastructure, something that is sure to be disrupted by Global Thermonuclear War, these cities starve.
War Day plus 365, best case, figure 300 - 500 million survivors, mostly in sub-Saharan Africa and rural Central Asia; worst case, closer to 10 million. In either case the progress of the last three centuries is gone & will be extremely difficult to replicate (easy to reach oil, minerals, etc. are expended, most remaining supply is technolgy dependent if one wants to gather them).