No, you should not put your Hydro Flask in the freezer because this will not make your water cold. If you would like to make your water or juice cold inside the hydro flask, you can place ice with the beverage instead. By doing this, you can make your beverage stay cold for hours.
There is a tendency that the materials that are used to create hydro flasks will not be able to take the extreme temperature inside the freezer. Also, the double-wall vacuum installation of the hydro flask is known to protect the liquid that will be placed inside, which means that the water will not freeze, no matter how long the Hydro Flask will be placed inside.
Yes, you can put your Hydro Flask in the freezer. The double-wall vacuum insulation of the Hydro Flask bottle will protect the temperature of the content of the bottle from the temperature of the freezer. This means if you put your Hydro Flask in the freezer, the bottle will not get cooler. If your aim is to get the content of the bottle cooler, it is best you transfer to another container that is not a vacuum insulator. After your drink gets cool, you can transfer to the Hydro Flask to maintain the temperature. You can also put ice cubes in your drink instead of putting the bottle in the freezer. In summary, the temperature of the environment has no effect on the temperature on the inside of a Hydro Flask bottle.