SHB...got 'em here just east of you. I usually can see a few in each hive from March through October, and after that I'm sure a few are still there, I just don't see them ;)
Problem? Not really. It stays cold enough late enough in the year that they don't really thrive, although they do overwinter in the hives.
Pollen patties early in the spring aren't a problem due to temperature, and they aren't really necessary any other time.
Same with wax moths...just don't leave unprotected comb around, especially comb with pollen in it and/or honey and neither should be too big of a deal.