Unless you have an Artesian Well, my aunt in Mississippi had one, running water in the house without electricity is kinda difficult.
Of course you could build a cistern on stilts and collect rainwater, to get the differential flow, but in winter it would be frozen solid..............
It’s easy enough to bring in a bucket of water for a flush, though; you can even melt snow to do it! I’ve done that in electrical power failures, summer and winter. ;)