The pressure will only change if the container is sealed, becouse as the temperature decreases, the fluid wil become more dense, which meansit will take less space, decreasing the pressure in the bottle. However, if the bottle is open air will enter and the pressure will remain the same. But, as mos drinks are water based, and water is breaks that law (it´s volume increases wheter you heat it up or freeze it down) the pressure will increase inside the bottle as the drink cools down and maybe explode the bottle.
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Yes, tempurature changes always effect pressure.
If you put an empty plastic bottle in a freezer it will start to collapse in on itself as the air inside condenses. If there is a liquid in it such as water, the air and liquid will start to condense. But once the liquid starts to freeze it crystallizes and expands inside the bottle. So just before freezing there can be a negative air pressure in the bottle. Once frozen there can be positive pressure. Depending on the ratio of liquid and air in the bottle.