Yes smoke can change the weather. Increased rainfall and mild acid rain are likely to happen down wind.
The cooling part : So I think you are asking about the albido (light reflecting property) of smoke. Yes, nuclear and volcanic winters are a thing, but most of that is from little particles in the upper atmosphere (like blot out the sun level of particles) now the smoke from fires won’t reach that high, so all of the sunlight they absorb will be dissipated into the air around them. And to make it worse, less trees also cause heating of the ground and air in that location. Here is an article that discusses [local cooling](https://www.nature.com/articles/ncomms7603) by adding trees to cities.
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