Simply leaving an air gap in a bottle will allow room for expansion, and most bottles can then be frozen safely, as others have stated.

BUT frozen water is basically useless you can get it out of the bottle drink it.

If you are presented with a bottle of frozen water, what would you do with it ? You need to turn it back into water and get it out of the bottle. How will you do that ? What equipment will you need ? How long will it take ?

When we winter camp, we turn the bottles upside down. If the bottle starts to freeze, the ice generally forms at the top (which is now at the bottom of the bottle), so we can still unscrew the top and drink the water.

Freezing bottls upside down may be better than right way up. If upside down, the ice can expand into the cylindrical base of the bottle, rather than be force into the constriction around the cap, thus increasing the possibility of a rupture.

But it looks like you are in much colder weather where the water will definately freeze solid. I've heard of people adding a little sugar and / or salt to the water to create a sort of anti-freeze. I've never tried this so I don't know the recipe or how effective it may be.

I guess you could test some recipes and the effectiveness with a bottle in your freezer ?

Perhaps there are some food engineers online who may have some experiance with food grade anti-freeze ?

Do I need to mention that vehicle anti-freeze is poisonous, so don't even think about using that stuff ?