In your climate, I would take it up a notch.  Place the heated bucket inside a junk bucket.  Drill a hole to run the cord through.  You've created some trapped air that will help keep the water warm.  You can also wrap the junk bucket with a non flammable insulation for better protection.  Now take a piece of plastic.  Cut it to cover the bucket.  A lid for a 5 gal bucket might work.  Cut a hole in the middle just big enough for them to get their head in.  Screw the plastic cover to the bucket.
  I did a similar design for horses where I had no power and 95% of the time it worked like a charm.  Or move south.