I have this exact problem as well.
Under very cold conditions, (cold start), i would get this bad sqeak when the fan is on the lowest speeds. This would come when I brake or put the car in gear. While in gear I would turn the climate off and the noise would vanish. When I turn it back on, it comes back again.
Seems to go away though when the car warms up. Figured the motor was going bad.
Thanks for the advice.