I'd do more diagnostics first. Are you losing coolant? If you're not sure, pay a radiator shop to do a pressure test, see if your cooling system is holding pressure. If it is, look for another cause.
Fog on the windshield is caused by moisture inside the car, which can come from many sources. Yes, check the heater coil, but it can also come in on your clothes on a rainy day, or from a window left open, a bad weatherstrip somewhere (the one around the windshield is a pain), or something spilled (possibly even in the trunk). In some cars, moisture can come from the AC condensor, if the drain lines get plugged up. It's winter, but when you run Defrost your AC may still come on. Don't do an all-day job if you're not sure you need to.