All living things are made of cells. Living cells generally contain water along with all the raw materials and structures that make the cell work.

Freezing usually damages cells because water expands when it freezes. Don’t take my word for that. Take a plastic bottle that someone was going to throw away and fill it most of the way with plain water. Use a marker to mark the water level, then put it in the freezer. The next day, take a look. The ice will be higher than the mark you made for the water level. The bottle may even have burst.

Animal cells just have thin membranes around them. When ice crystals form, they destroy the cells. That’s what frostbite is.

Plant cells have cell walls outside their cell membranes. This may protect the cells from bursting, but plants that are not adapted to freezing can die at freezing temperatures. Many bacteria have tough cell walls that resist freezing, so freezing food does not kill most bacteria, it just sends them into a sort of hibernation. When the bacteria warm up, they’re ready to start reproducing and causing trouble again.

Walls are not the only way to protect cells from freezing. Water can get very cold without freezing if it has certain things dissolved in it. Cars need circulating fluid to cool engines. People add antifreeze to a car’s radiator water to keep it from freezing. People in cold climates sprinkle salt or other things on sidewalks to melt ice and keep it from forming. Some cold-adapted species have types of antifreeze in and between their cells so that they can be colder than 0 Centigrade or 32 Fahrenheit and still not freeze. Some species remove a lot of the water from inside their cells and the spaces between them so that there is less ice to form.

There’s a great article about this at: here

What might be some of the drawbacks to making anti-freeze or letting yourself freeze?

You may want to study animal physiology.

Whether an animal can survive freezing is going to depend to a large extent on how long it has been frozen. For instance, you can stick your hand into liquid nitrogen for a fraction of a second and be fine. If a fish is frozen for a short period of time, it may still be alive when it thaws. This is because there wasn’t enough time for the ice crystals to damage the fish’s tissue and ultimately kill the fish. However, if you put a fish in a freezer, it would almost certainly die fairly quickly.

There are animals that can survive lower than freezing temperatures because they have special “antifreeze” molecules in their blood that stop it from freezing. So an animal could be partially frozen, but there aren’t enough ice crystals to kill the animal. Some animals that exhibit this behavior are turtle hatchlings, beetles, moth larvae, and wood frogs. An interesting example is the microscopic water bear which can withstand being completely frozen, but that’s because it can also completely dehydrate itself as well.

So a fish in a block of ice would certainly not survive if it was completely frozen through. As for the fish getting frozen in the winter and thawing in the spring, this is not what actually happens. When a lake or pond freezes, only the top layer freezes and there is still liquid water underneath. So the fish survive in the liquid water underneath the ice which is very cold, but not frozen.

There are animals that have chemicals in their bodies that allow them to be partially frozen and still survive. There is still a minimum temperature, and generally that temperature is high enough that the animal in question is not a solid block of ice. The problem is that ice has a lower density than water, meaning that water expands as it freezes. This means that any container of water that is freezing (like, say, a cell membrane) will burst as the water changes to ice. This tends to destroy any living tissue that is allowed to freeze entirely.

Now, there are animals, called tardigrades, that can freeze entirely, but they do it by being able to survive being completely desiccated so that there is no water available to freeze. It's still pretty amazing though (these are animals that can withstand the vacuum of space!).