How does carb heat increase the risk of dirt ingestion? In this question about turning off carb heat just before landing, one of the justifications for doing so is to reduce the likelihood of ingesting dirt into the engine.
How does carb heat (or the lack thereof) affect the amount of dirt that might be ingested into the engine?
I am not a pilot, but I would think there would be some sort of air filter like there is on a car/truck. Also, I would think that, if anything, ice in the carb (while Not Good™/potentially fatal, especially on landing), would reduce the likelihood of getting dirt into the carb by acting somewhat like a filter - i.e. giving dirt a place to land before making it all the way through and into the cylinders.
Carb heat is not only about heating the air going into the carb, it's also a meant to be an alternate air path in case the air intake becomes fouled or the air filter gets clogged by debris, snow or ice. Fuel injected airplane engines typically have an alternate air intake that bypasses the air filter for the same reason, it's part of the checklist to test the alternate air. 

The reason there isn't a separate filter for the carburetor heat air is that the same thing that clogged up the main filter could clog up the secondary, it's better to have unfiltered air for a short time than take the chance of losing your engine.