Wifi landline implies a data connection.
There are literally hundreds, if not thousands, of cheap freeze alarm type devices that all work over standard internet connections.
Buy a cheap (eg: in the $100-$150 range) UPS. Plug your router into it, along with your freeze alarm and/or other sensors. *Most* of the time when the power goes out, data networks stay up for a while (they have their own UPSes). With that setup you can get alerts when the power goes out as well so you have some idea how long you didn't have power for, and the odds of things freezing.
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