Here's my guess, see if my reasoning makes sense:
1. Something is causing a massive current draw- evidence:
A. the alt belt is squeeling and RPMs dropping as engine tries to turn heavily loaded
B. the heater blower is slowing down indicating possible dropping voltage
What could draw so much current that it stresses the alternator belt to the point of squeeling?
What could draw so much current that it pulls the voltage down in the whole system?
What has wiring going to it sufficient to pass this kind of current?
The only thing I can think of is the battery itself. How about a battery that is intermittantly internally shorting? Only does it at real low temperatures, maybe.
Just an educated guess now; but the pieces seem to fit, or at least they can be made to fit.
Often wrong but never in doubt.