The general wisdom about water is: it must be below the frost depth for your location, then any water at that depth, even during the coldest periods won't freeze. Usually we're talking about water coming in from a water line, and the pipe is sealed. In the case of earthship cisterns they're open air in some sense, though covered with pebbles at the riser. Dan Richfield showed his cisterns and how: 1) the top of the cisterns were below the frost line (18" in Taos, NM); 2) the cistern was insulated. So even though the cistern was open air with air holes going down into the cistern, the water in the cistern would theoretically have enough mass to resist freezing. I'm taking that one on faith that it's going to work. Mongolia has a frost depth of about 2 meters (almost 7 feet). As long as the surrounding soil isn't frozen and the cistern(s) is insulated, then I guess that's enough. Temps drop below freezing everyday around early November (almost now), rivers freeze into solid blocks until the end of March. During those 5 months or so, I don't plan on collecting any precip. Maybe if I'm worried about it, I could put some insulated cover over the cistern catch on top.
I was considering having something like the equivalent of 2 stacked garbage cans full of pebbles as a catch. That may be so many pebbles to drip through that some may be lost to evaporation. Maybe like many earthships I could do the small amount of pebbles (about 12"?) in a plastic drain thing (on top of a pipe?) and just put an insulated cover over that during winter. Maybe just the depth alone would protect the water from freezing.