I suggest you take a look at "Climate Impact of a Regional Nuclear Weapons Exchange: An Improved Assessment Based On Detailed Source Calculations" [1] or similar papers. Scientists have run nuclear bomb simulations (and these codes are rather good), used them as input to fire simulations (well validated through forest fires) and then done climate models and radiation (in the sense of "light") transport calculations of the atmosphere. The result is "fucks with the polar regions, but humanity is going to be fine".

[1] https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017...