I've used cozies, but they only work slow the freezing process. A thermos is definitely the most sure-fire way. In the really cold weather we've had the last 3 or so weeks, I made three trips and used my thermos on each. It is nice to have hot water for soup or cider at lunch to help warm up again.

Beyond that, boil a liter and put it in your nalgene, then sleep with it. Mine made it through the night each time and gave me enough water to reboil and add to the other containers in which some water froze (excluding my thermos, which was fine). This let me thaw all the ice in all containers, a huge benefit.

The other big plus is wide-mouth bottles. I don't carry full-size nalgenes usually, but will do so in sub-freezing weather. The wide mouth is easy for pouring boiling liquid and they stand up well to such heat.