Probably a bad solder joint, and the cold causes things to shrink enough to reestablish electrical contact, if only temporarily.

The plastic bag would be to keep moisture out, especially when you take the now cold drive out of the freezer and room moisture now wants to condense all over it.

All brands of hard drive can fail. I use Western Digital and haven't personally had any fail on me. I also have about 25 drives. Anecdotal evidence is not very good for judging reliability. The take home lesson is always have a backup. No brand is so reliable you don't need a backup.

I use a trayless enclosure so I don't even have to buy a $20 tray. I store the drives in Disney-style VHS cases with some extra foam to make a tight fit.

I'll second Ervin's suggestion, about swapping the electronics.

I have done this a few times, with identical electronics, and had sucess everytime.

I tend to keep some similar "electonics", for just this occasion, and have gotten what I needed, then tossed the drive, sans the electronics of course.

I've also tried the "freezer" application, and had sucesses with that too.
Ususally keep it in overnight, let it thaw out slightly, in the bag, then straight into the powerup mode.

I'm an AV guy who works in an IT dept, so have come across similar issues.