We don't get as cold as you do, but there's a ~15x20ftx4.5ft cement reservoir on my parents land, presumed built by the previous owners who homesteaded on the property from shortly after WWII; more than 35 years old at least, possibly more like 60.
While it's rare lately, 15-20 years ago hard freezes were common; we could skate on the ponds as often as not. This reservoir is 3/4 above ground, and ices over freezes an inch or two thick for a while even in recent mild winters. It still holds water just fine.
A greenhouse would definitely help prevent freezing, though how much would depend on the details of both greenhouse and climate; I don't think the barrel of water in my tiny unheated greenhouse froze last winter, but if it did no harm was done and I didn't even notice.
One year, I forgot to drain my 275 gallon IBC tote water containers and they froze solid. When they thawed in the spring, metal cages were seriously bowed outward but the plastic parts retained their ability to hold water. The drain valves were also functional, but a bit harder to operate.
Hi... here in Northern New Mexico, we can get 10-15 below zero F. and lots of nights in the teens.... and our 4,000 gallon poly tank has a 2-3 inch thick layer of ice on the top of the water and some along the insides if the tank, (where it is above ground)..... I buried the bottom 3 feet of the tank, wanting the exit opening (for water to gravity fed out), to be buried 3 ft....... the core of water and the bottom of the tank.... never freezes..... but if you had a small tank... say 500 gallons and didn't bury it... it might very well freeze..... to where you wouldn't have any water usage....
If the pool is directly on the ground, it should get earth heat from below (except around the perimeter where frost would get under a little ways). A pool cover on top could help insulate it and capture sunlight (when there isn't snow on it) Diamond pool cover. If you dug down a few feet and insulated around the perimeter then the frost couldn't get under it and the earth heat would be under the whole pool. And you could surround it with straw/hay bales for more insulation.
The permie formerly known as "Mike Jay"
"Hundreds of years from now it will not matter what my bank account was, the sort of house I lived in or the type of car I drove... But the world may be different because I did something so bafflingly crazy that it becomes a tourist destination"
We don't have time for this. We've gotta save the moon! Or check this out: