Hi Ross: Good points in the previous posts. The reasons you are getting so much moisture on the inside of your windows in the winter are: 1. You are generating lots of moisture in the house. Previous posts have named several sources: moisture rising up from a damp crawl space; many showers/hot water boiling, lots of people breathing and perhaps a ventless gas log set. 2. Your house is "tight", meaning it lets little fresh air in around windows and doors to replace the humid air, and 3. You are not using insulated windows (or exterior storm windows). Meaning, the glass is the coolest spot inside your house, so the excess moisture naturally condenses there.
Possible solutions: 1. Reduce interior moisture sources. Crawl space plastic sheeting; stove exhaust during cooking; bath exhaust during shower/bath; slight damper opening when using ventless gas logs.
2. Extract moisture from the air. Best way to do this is to run the central fan. This will force the interior air over the A/C (assuming you have central A/C) evaporator aluminum fins, which will acts as a big dehumidifier. Or, as you suggest, you can run a dehumidifier, but this will be an expensive alternative.
3. Install insulated "thermopane" double glazed windows or exterior storm windows.
4. Install a heat exchanger. This is now required in many new housing areas. It passes inside air over a series of multi finned heath exchanger coils, then passes the inside air to the outside, bringing in outside air and passing back over the heat exchange coils, warming the air up.