There are not enough nukes luckily. 80% of humanity would be wiped out but remote places like Australia, Siberia and parts of Africa would be unaffected, so in theory humanity could survive. The biggest problem is that potable water would be a problem since you don't have any infrastructure left to clean it, but of course those remote locations could fetch clean water if they are lucky. In the last centuries we got child mortality rate really low, that would probably go back to 40-50% like in the middle age. The life in the post nuclear war world would be very difficult, you probably know what I mean if you ever played with Fallout.