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...

We have detonated 2000 bombs in testing. So "just a few small nukes" is not enough to start any atomic winter.

https://en.wikipedia.org/wiki/Nuclear_weapons_testing

But not over forests or cities - which burn.

We have tested that also. During 1945 we burned down 69 cites and killed 800 000 in Japan. The two small nukes was only 5% of the smoke.

The result was at most an cooling of the global temperature of 0.1-0.2 Celsius. But the "multiple uncertainties mean we cannot say for sure".

https://www.carbonbrief.org/guest-post-did-bombing-during-se...

So we need about 5-10 times larger bombings when ww2 to cool the global temperature with one degree. But we have increased the global temperature with one degree thanks to global warming. So you need at least 10-20 times larger bombings then ww2 to get a tiny atomic winter. And probably a lot larger to get any catastrophic cooling.

Well we’ve done 2 over cities closely spaced with each other and also following a firebombing campaign that burned a lot more cities. If a burning city or forest was all that was required for a nuclear winter we’d have had one long ago. Forests burn without the aid of nuclear weapons.

To get to nuclear winter levels of ash and dust you probably need dozens to hundreds of detonations and burning cities.