It depends on where you are, how the house was built, and how cold it gets.
Where I live, with many homes plumbed on the assumptions from "normal" lows, we have plumbing freeze-ups in some houses when temperatures drop below 0 F for a day or more (about 20 F below "normal" lows) even while the occupant is running the furnace full time to try to maintain comfortable temperatures in the 65F to 70F range. For homes on slabs, kitchen plumbing sometimes comes up in outer walls, and sometimes long runs are made in the attic, which will stay above freezing with heat losses during "normal" lows.
Crawl space plumbing does better if vents are closed to contain heat, basement plumbing seldom freezes in a house heated to any temperature above freezing, but you have to watch out for runs in outer walls.
Then you need to re-think your assumption that the house is heated to NN F temperature. One January I took a cruise to a warmer place, and an ice storm took out power for several days, followed by a near zero to sub-zero spell. The service line to my house was pulled down by falling limbs, so power stayed out even after the distribution system was brought back up. Damage from water running out of burst pipes exceeded $10,000 and I had to pay the city several hundred dollars for the water that filled the house before I got home.
I left a house empty but climate controlled (60F in winter and 85F in summer) while working on another continent for two years (college daughter needed to come home to it) but I also had daily walk-arounds and weekly inspections with exercise of plumbing and adjustment of lighting timers. It cost about $100 a month (on top of monitoring fee) but it was worth it, as the inspections caught a couple of plumbing problems that could have gotten quite expensive. Thinking I could just walk away from a house for 10-12 days in winter, after retirement, turned out to be a much more expensive mistake.
I grew up in Michigan. Houses there, at least those I lived in and summer homes particularly, were designed to be winterized cold, just like a RV. Water supply can be cut off, all lines drained. If your house can do that, I advise it, even if you don't plan to let it go cold.
If you don't want to winterize, rather leave it warm, then have somebody watching the house, checking on it, with authority to spend for repairs needed to protect the house.
Tennessee is not Michigan (where I let a winterized empty house go into cold storage) or NE Oklahoma (where winters are not usually cold but can get Minnesota cold for a few days to a few weeks). So my experience does not fully translate.