This is why Chernobyl was more toxic than a detonation. Above 1 Mt the nuclear dust gets dispersed high in the troposphere. Chernobyle was a nuclear burn pit with low level spread of nuclear dust all over.
This dust which spread out tended to accumulate in concentrated form in snow melt water bassins. I directly drank very high dose of concentrated radio-water in the Alps. I got two days of radiation poisoning sickness followed by gland growth a few weeks later.
The thyroid being particularly hit, an immune attack on the thyroid fueled thyroid which fueled more metabolism further stimulating auto immune reaction. The result was that my body ate itself including the gland growth which them shrank.
Suffice to say I must still have strontium in my bone and still risk bone cancer eventually, not sure. It has been 30-40 years since then and I risked death without any treatment after significant exposure. I however survived a direct internal radioactive hit they no one would suffer if taking cursorial fallout contamination and ingestion after a nuclear exchange. Bombs do not pollute as much, let alone high megaton types. And the Nuclear Winter is a myth. These big bombs do not have the fall out drop back down on us, it spreads high stuck between the troposphere and higher layers much like Cyrus clouds.
The initial blast within a certain radius avoided, it is totally survivable. The only danger is the chaos resulting from lack of electricity and law enforcement. This is what kills a majority of the people, the disorganization, not the kinetic effects.
Australian study even noted that smoking is far more noxious and radioactive than a nuclear fallout, so much that in Australia cancer would be reduced due to lack of available tobacco.
*. I however survived a direct internal radioactive hit that no one would suffer if taking cursorial fallout contamination and ingestion precautions (dust mask and rain coat to wash after going outside) after a nuclear exchange. Bombs do not pollute as much, let alone high megaton types.