Most hard drives are not designed to operate below a certain temperature, so you should be letting the inside of the car warm up before you even try to operate the Phatbox. Sounds to me like the drive heads are stuck, though I'm not sure that would be caused permanently by cold weather. You might just have a defective drive.
You can use the hack and repair CD to format and repair the drive.
If that doesn't work, try getting a warranty replacement.