Yes you can swim in a water tower if the water level is low enough to allow room for your head to be above the water.
However you should never enter any water tower without proper training and the proper breathing and diving equipment as it's very easy to die in a water tower.
There was one guy who was cleaning and inspecting a water tower and he died and they had to remove his body from the water tower.
Water tower cleaners and water tower inspectors will put on diving equipment and dive and swim around in the water tower while it's in use.
But those people have special training and have the experience and equipment to safely dive in and swim around in a water tower.
The reason water towers do not freeze is because the water tower is constantly draining and refilling through the day.
The water in the water tower does not just sit there and not move and so it does not freeze just like when you leave your water faucet running it helps to keep the water from freezing.
Moving water is harder to freeze than water that is not moving.
The air up above where the water tower is is also not as cold as the air down on the ground.
So it's warmer above where the water tower is.
I've heard of a water tower freezing before in some town but it's rare that it happens.