Water pipes can freeze at around 30 F or below but usually won't burst open until the temperatures dip to 20 F or low which is the danger zone for burst pipes.
You should leave water dripping on really cold days and nights to avoid pipes freezing up and bursting which can cause some major damage.
Also insulate any exposed pipes and keep cabinet doors open where pipes are to allow heat into the cabinets so that the pipes won't freeze up.