Yes, it is dryer in Chicago in winter (our summers are sub-tropical and very humid) than summer - one of my cousins commented on how she'd forgotten how dry it is in winter, plus a lot of heating is done with with steam, which leads to dryness inside, which leads to bloody noses etc without proper humidification.
It would make sense it's the dust mites - I had a lot of problems as a kid, but don't seem to as an adult. I would think mountains would be bad for allergy sufferers since the altitude would cause problems. In olden days allergy sufferers were sent to Arizona, but with the massive population increases the humidity has increased as have the allergies from imported plants.