When you put a water bottle in the freezer, it does not actually absorb the cold of the freezer itself. Instead, what happens is that the water bottle's temperature equalizes with the surrounding cold air in the freezer.
When the water bottle is placed in the freezer, it has a higher initial temperature than the freezer's air. Heat naturally moves from a higher temperature region to a lower temperature region until both reach equilibrium. So, the heat from the water inside the bottle transfers to the surrounding air in the freezer until both the water and the air reach the same, lower temperature.
The process by which the water bottle gets cold is technically the result of heat transfer, where heat moves from the warmer object (the water in the bottle) to the colder object (the air in the freezer). The water in the bottle loses heat until it reaches the freezing point, at which it turns into ice.
It's important to note that the freezer itself doesn't lose coldness during this process; rather, it maintains its temperature, continuously keeping the environment cold enough for items to freeze.
So, when you take the water bottle out of the freezer, it has reached the same temperature as the freezer's air, making it feel cold to the touch.