The two real options, and why there isn't a third
Keeping the heat on at a safe minimum — generally well above freezing — protects the plumbing, but it means an ongoing utility cost and, usually, insurance requiring the house be checked on a regular schedule while it's occupied by no one. Fully draining the water system (plumbing, water heater, any exposed lines) removes the freeze risk entirely and can lower the ongoing cost, but it needs to be done properly, generally by someone who knows the house's specific plumbing layout, not as a quick DIY afternoon.
Turning off the heat without draining the system is the option that causes the damage — it's the default that happens when nobody makes an active decision, and it's the one to avoid specifically.
What else genuinely matters, once heat or draining is handled
Insurance needs to know the house is unoccupied — most policies have specific requirements once a home sits empty, sometimes including a schedule of in-person checks, and skipping that notification is a separate, serious risk on top of the freeze question (see the note on estate house insurance below). Gutters and downspouts clear of debris prevent ice damming, which can force water back under the roofline. And a working smoke and, where applicable, carbon monoxide detector still matters in an empty house — a small, cheap thing to confirm before winter, not after.
Who to actually call
A plumber for a proper drain-down, an insurance broker to confirm exactly what an unoccupied policy requires, and whoever's checking on the house regularly to actually go check — those three calls cover the real risk. None of it needs to wait for a bigger decision about the house's future to get sorted first.