If you are in deep snow, or if the ground is not frozen, you can bury your water. I've buried water in a snow bank (it was deeper than 18 inches) over night in a pot w/lid and woke up with just a skiff of ice on the top. I've never done it in the ground, but I've got to believe it would work in that as well assuming you can dig down two feet or so.
Backpacking may be a little different then your camp. Using the cooler previously mentioned is not a bad idea if you have one. It can insulate both ways. Be careful about filters freezing as they can be damaged. If there is any question I sleep with mine. If it is to cold, boiling is better than risking the filter IMO, and its nice to put the boiling water in the water bottle, which goes into a sock, and then into my sleeping bag. With my small one man tent it has to get significantly below freezing for the inside of the tent to get below freezing. Depending on temperature I sometimes have all kinds of things in my bag. Water, water filter, fuel bottle, batteries, camera, GPS, clothing, etc. I did have my boots freeze solid one night. Left them in the vestibule, slightly damp inside from perspiration and outside from walking in snow all day. That was fun.