We have detonated 2000 bombs in testing. So "just a few small nukes" is not enough to start any atomic winter.
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.
To get to nuclear winter levels of ash and dust you probably need dozens to hundreds of detonations and burning cities.