If the beer freezes, it's too cold! It's hard to say, as the beer won't necessarily drop to that cold temperature, but I would be very hesitant to put it somewhere that cold. Fridge temps (35-40) are great, but you could probably get away with 30 degrees.
I have heard some horror stories on here about doing exactly what your talking about. The problem for the most part is using a glass carboy. The beer will freeze from the top down. When the top inch of the beer is frozen is prevents pressure from the water expanding to release through the airlock. All that pressure from the expansion will break the bottom off the carboy. It's pascals law of hydraulics in action. I'd assume it would push so hard on a bucket that it would cause a crack.