On a cold winter day, the water will gradually lose heat and get colder. But you can take easy steps to mitigate the effects of freezing.

When you leave home, consider filling the bottle with hot water instead of cold. This will buy you some time and delay the effects of freezing. Essentially, your loading up the water with extra energy and that energy will slowly dissipate

Store the bottle inside your pack surrounded by soft things like clothing. They will provide insulation and slow down the loss of energy and heat from the water. Storing the bottle in an outside pocket has the advantage of convenience for quick access, but on a cold day, the energy loss will be much faster.

Store the bottle upside down (and securely closed). Why? Because freezing always starts at the surface of the water. If the surface is swishing about at the top, the top of the bottle and lid will freeze, and it would be harder to unscrew the bottle and would entail encountering ice first.