Frozen water lines, what should I do with my electric hot water heater?
What is the temperature where the hot water heater is? The tank is big and insulated and while it will take longer to freeze, if the ambient temperature is below freezing, it will eventually freeze. 

When pipes freeze, there is much less water volume so they will freeze much faster. Also, copper is an excellent conductor, so standing water in copper pipes will be very close to the surrounding temp.