Mark brought up a good point about turning off the furnace humidifier. Even if it has a humidistat it may fail or measure dry air from another area.
The problem with venting in the winter is you pay to heat the new cold air coming in. An HRV is a good investment. Dehumidifiers are okay in some cases, but they may not be able to keep up. If you are planning to buy one you can hit the second hand stores, news papers, Craig's List, and Kijiji as this is the time of year people typically turn off the A/C and dehumidifier and turn on the furnace and humidifier.
What is the current humidity level? It should be below 65%, preferably 55%. The problem could be that your windows aren't as insulated as they could be. It doesn't take a lot of vapour in the air to make cold windows sweat. A second layer of that plastic you put over the inner window gap with a hair drier will help, but it isn't very convenient. Once your furnace kicks in it will burn off a lot of the humidity, assuming you have forced air gas (FAG). Burning wood will add humidity unless you have a wood stove.
It isn't an easy fix, but covering the tank at night would help a lot. As the room gets cooler at night, more water evaporates. Just don't forget to take the styrofoam off of the tank in the morning before the light melts it
Eliminating the other sources of humidity in the home (basements, bathrooms, and kitchens) can also help.
You could always use it as an excuse for your family to move into a well insulated log cabin with a nice big wood stove. The fish part of the family