I'd be concerned about weakening the plastic in the gatorade bottles. It's a different material, thinner, and not as durable. Definitely try it at home to see what the bottles do. I've deformed lots of plastic doing heat experiments with them....and sometimes even I had to laugh at my foolishness. Be sure it put them in thick socks or some other insulating material...thick enough to protect you and thin enough so the heat comes through.
A side benefits of using "nalgene" bottles, if you have enough insulation your breakfast water and instant oatmeal water for breakfast is ready. On one trip it hit -8 F on us. Since my water bottles were keeping me warm, I was the first to have a hot drink and breakfast the next morning.
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