A faucet drip during extreme cold weather can help prevent a pipe from bursting.
Only pipes vulnerable to freezing (ones in an unheated or poorly insulated exterior wall) should be opened. The drip can be very slight. Make sure both the hot and cold contributes to the drip, since both are subjected to freezing. If the dripping stops, leave the faucet(s) open, since a pipe may have frozen and will still need pressure relief.
It’s also a good idea to keep cabinet doors open during extremely cold temperatures.