First...TURN OFF THE WATER SUPPLY!
(Actually, as mentioned above, turn off the water heater first.)
The big problem to avoid and manage is loss of heat.
Ask yourself how that can happen.
1) power failure
2) furnace failure
It the problem is a power failure you will need a notification system that is immune to the loss of power. A temp alarm or monitor that relies on the internet will not work if the modem/router go dark when the lights do. A universal power supply (UPS) can provide battery power for these for a while.
My house has a fire alarm system that uses a land line to report. Whenever the power goes out I get a text. When it's restored I get another text. No power means no heat so the clock is ticking after the first text. The phone lines can go down with the power lines if the tree branch is extra angry. In that case, I am vulnerable.
We also have a gas generator and 10 gallons of fresh, stabilized gas with instructions ready to wheel out for use. So far the generator has done a great job. We have had zero power failures since we bought it!
If the problem is a furnace failure my cold alarm will dial out through the alarm panel and notify my family and me. So far I have not gotten that call but I have a plan in place for it.
I do not expect a speedy resolution to a furnace failure. The repair folks may be busy addressing other emergencies. There is a part on my propane forced hot air furnace that I'm told is a frequent point of failure. I have that part and a paper service manual ready and waiting next to the furnace.
To slow the cooling of my house I have six electric space heaters with a folder of instructions. The instructions include pictures I have taken with the space heaters exactly where they should be positioned to provide the most heat to the plumbing.
The generator and space heaters require a person to go to my house and do the work. I have two sons and each one lives an hour and fifteen minutes away. They know what to do.
My friend four doors down had two freeze ups at his house. Both times the toilets all cracked and the refrigerator defrost drain got screwed up. He wisely had his water turned off. He now has a temperature monitoring system that relies on the internet. He has no UPS.
Another important thing to do prior to cold weather is disconnect the hose from the hose bib outside. The hose bib is likely a "sill cock" which has it's shut off valve seat deep enough in your cellar so it won't freeze. When you turn the handle outside it closes the valve inside the cellar. Any water remaining in the section of pipe from the shut off to the outlet will drain out. That design ensures that the section of pipe will not freeze.
If you leave the hose attached it cannot drain out. If it freezes the pipe will split between the valve in the cellar and the cellar wall. You will not know that this has happened. When you go to use the hose in the spring your cellar gets treated to a shower!
I hope this helps!
(And yes, I am retired.
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