I'm skeptical that we would see much effect from an exchange of 50 weapons; the year 1962 saw 178 detonations.[1]
The trend in nuclear weapons has been for lower yields over the last 45 years or so. The reason is that advances in CEP precision due to better guidance systems means than huge yields are no longer necessary in order to ensure destruction of the intended target(s).
'Nuclear winter' is a completely unsupported theory pushed by Carl Sagan and the Union of Confused Scientists. Recall that these same people pushed 'the coming Ice Age' in the 1970s, 'global warming' until even their jiggered data was so obviously wrong that they renamed it 'climate change', and also predicted 'nuclear winter' effects from the burning oilfields during the first Gulf War - which never materialized, of course.
https://en.wikipedia.org/wiki/TNT_equivalent
* The total energy of all explosives used in World War Two (including the Hiroshima and Nagasaki bombs) is estimated to have been three megatons of TNT
* The total global nuclear arsenal is about 30,000 nuclear warheads with a destructive capacity of 7,000 megatons or 7 gigatons (7,000 million tons) of TNT
And TFA talked about a nuclear winter from burning cities when using a hundred Hiroshima bombs, not the US/Russian arsenal. We ought to have learned about those effects, just from WW II.