The main two issues are wildfire and inversion.

As you said, Boise is in a sort of bowl (more of a valley), in the winter, a cold air system can get trapped in the valley by warmer air in the mountain area. This can lead to some pretty bad air (not nearly as bad as wildfires, just not very fresh). To me, the bigger complaint is about not seeing the sun for days. Idaho has a lot of sun throughout the winter, so it's noticeable. It isn't all winter, just a week or so at a time a few times per winted, depending on weather.

But otherwise, Boise's air is quite clean.