Cold weather rarely has a negative affect on electronics or motors. Poor solder joints and weak components can be placed in a freezer and will tend to operate after failing in room temperature. I would guess that your problem is due moisture and not the cold. Does the HU operate when you first turn the car on and then fail after running the heater?
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 2003 Maroon Alero GLS Sedan. (Purchased new in 2003 with 18 miles, and sold in 2006)
2004 Toyota Corolla LE (Purchased new in 2003 with 87 original miles)
2007 Toyota Camry LE (12 original miles)
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