If the fridge in question is equipped with 1,1,1,2-Tetrafluoroethane. Worst case scenario is the compressors lubricants become unable to do their job in the cold temperature reducing the efficiency of the compressor, eventually damaging it's components from friction, also may cause motor start up trouble due to insufficient lubrication. There may also be some inefficiency introduced as the gas may begin to liquefy to soon settling in the compressor washing away the lubricant as well.
The lower operating temperatures I've seen recommended for refrigerators is ~50-60 degrees Fahrenheit.