If you still have running water, allowing a trickle of water run from each faucet will keep your pipes from freezing/expanding, for the reasons already mentioned.

Draining the water from your pipes will keep them from bursting because there is no water to freeze/expand to split the pipes. The piping freezes and that should not split them.

Leaving the faucets open even though you can't drain the water will still allow some room for the freezing water to expand, thus keeping your pipes from splitting.