Depending on where they sit it won't matter if it's a Platypus or a Nalgene, it's going to freeze though personally I have never had either style freeze on me down into the teens. It just depends on where you put it and a bit of common sense.

One thing you DO have to watch with ANY water filtration (save for tablets) is not to let the filter membrane freeze. It will will crack and effectively be useless.
Keep it in a warm spot or tucked in a jacket (since they are tiny) and no issues.