When I say "coolant" I mean ENGINE coolant (radiator water) - not A/C refrigerant. Check the water level in the radiator overflow bottle and make sure it is about 1/3 full with a cold engine. It it gets too low, then of course you might overheat the engine, but if it's just "sort of" low, there may be enough water to keep the engine from overheating, but not enough to supply the heater core with warm water.

Given the time of year, I think I'd attack the heat issue first. What does the temp guage read when the engine is running?

If you follow the power wire from the compressor, you should find a disconnect plug. You could disconnect it, that way you could run the defroster without blowing the A/C & window fuse. Then tackle the compressor problem when you get time. (Yes, you were right by the way - isn't it just dandy the way they put the compressor and the windows on the same fuse?)