Water is ~ 1000 times heaver than air so for a fridge, removing the water is the same as letting out air 1000 times.
Freezer is worse because there is also the phase change in the water. But having ice is useful.
Professional cooler packs can have that point down as far as -35 Celsius.
Adding salt to your water will substantially lower the thawing point and it’s still cheap and widely available.
If you want to prep for cases when you need water you’d be better off keeping your freezer cold with a suitable medium and have a few 30liter buckets of water with some sort of additive that prevents spoilage (silver ions for example) or have some packs of bottled water around.
You would have a larger thermal mass but the same surface area so it should keep for longer.