If the water in the pipes is standing still and not moving then when the temperature outside falls to 30 F or below the water pipes in my home begin to freeze up.
If the water is flowing through the pipes it still can freeze up but it takes a colder temperature as in 15 F or colder for the water to freeze in the pipes.
This is why it's recommended to leave your water pipes flowing at a small steady stream through the faucets to prevent frozen pipes from occurring.
The little increase in the water bill is nothing compared to what the bill will be to have a plumber come fix broken water lines or the cost of the damage done from the burst water pipes.