In those cold temps you can just remove the fan and drive it without fear of overheating, providing your not working the engine hard. I would be inclined to try that first, the fans for the most part are a pretty reliable unit and not very failure prone. I've seen several in the 2nd gens go 300k+ miles. If it doesnt sound like a 747 all the time, its likely fine. For your engine to be that cold it would likely have to be locked all the time, and I dont know if even then it would keep your temps that cool.
The a/c compressor is used year around to remove mositure from your hvac system. If you don't have a/c, I would bet that is the culprit of the frosty windows inside. The recirc button idea is your call, but IMO find the problem, and that truck will roast you out once its warmed up. Even at 2 degrees this morning, I had my heat knob at the 12 oclock position going down the road and no frost issues inside at all.
As for the cool engine temps, you may try a manual gauge just to verify actual temps. With the radiator cap removed do you see good coolant flow when the stat opens? FYI all that grease your seeing is from the breather tube on the front of the engine. They can get so plugged up it will cause overheating problems in the summer. Probably not on your list of to do's at the moment, but your probably going to have to pull the radiator and degrease it at some point.