In my house, the problem is too much humidity, not too dry..
Here in the Bay Area, the main problem is not indoor air being too dry, but rather it's too humid. Even in winter, the humidity can be a problem. Our maritime environment, coupled with temps that are usually above freezing, mean that conditions are usually on the damp side.
Most indoor humidity comes from beneath the home, from the earth. It's an unlimited supply. Tighter construction - better sealed windows and doors, vapor barriers, etc., mean less and less of this earth-sourced humidity can escape to the outdoors. In serious cases the humidity condenses in cold attics and crawl spaces, actually creating rain in these spaces and rotting wood beams and rafters - not to mention creating ideal environments for toxic black fungus.
Part of the solution is ample ventilation of kitchen and bath spaces - the prime sources of non-earth sourced indoor humidity. Another solution is to install a vapor barrier over the earth under the home. Often plastic sheeting will do the trick, but some even recommend paving over the crawl space with concrete over the vapor barrier to make it a more permanent fix.
Obviously in other, colder winter climes, dry indoor air can be a problem. However, based on my experience, I would not try to introduce more moisture inside the home without first measuring the relative humidity to make sure it's fallen below about 45% first. If it's 50% or higher, there should be no need to add more moisture, and if it's above 60%, then one shoudl investigate ways to dehumidify the indoor environment.
For getting rid of dust raised by forced air central heating, check out the furnace filters from 3M (Filtrete) and use a good HEPA filtered vacuum cleaner.