I could see higher rolling resistance leading to poorer fuel efficiency and greater exhaust emissions. Though, I imagine temperature inversions, home heating (particularly via wood), etc. have a much greater impact on Winter air quality.
Faster tire abrasion causes
a) more particulate pollution from tire residual (which can be massively worse than pollution from exhaust in cities)
b) more exhaust pollution from worse car mileage
This is more or less correct; a car with studded tires will average around 20kgs of asphalt dust over a normal winter season.