Original Message

I'm now retired but flew type twos for many years. Alaska, the western states and Mexico. In answer to your question, no breathing protection . You just breath the smoke. I hear that some type three machines have AC. 
Flying into heavy smoke is a bad idea simply because fire fighting is VFR ,low altitude and  usually involves higher  nasty terrain right where you are working.

Dont be too critical of those County and Cal Fire guys, most of them were flying fire contracts for years before landing those good jobs.

Stay safe,

Another Old Guy