Consult your local regulations of course. But frozen pipes are no joke and can turn a brand new, perfect home into a condemned tear-down, rebuild in a matter of hours.

For those in that situation, turn off the water to your home and drain the pipes. Bursting pipes can do massive damage to your home and make it uninhabitable during the rehab.

Two units in my apartment building already flooded because they didn't trickle their water. Trickle means a tiny trickle of drops, not leaving the tap running. Use common sense, not FUD.

Be that as it may. Frozen pipes can be catastrophic.

Honestly probably better to store some water, run your pipes in a tiny stream, and then if you lose water at least your pipes will be drained.

There are issues with restarting a forced hot water furnace if you drain your pipes entirely.

Issues? You just need to restore water in the circuit and vent the air trapped in the radiators... really