Is the problem of cryonics only the pressure?
The major problem in cryonics is that when an organism is frozen, all of the organism starts freezing. The cell start expanding since ice expands too. The sharp edges of the ice crystals can destroy a lot. Also, your blood would freeze. Again, the sharp edges of the ice crystals would destroy major blood vessels. That is why currently, they have to insert antifreeze into the blood, but it still might not be effective.

Now, to answer your question, many cold-blooded organisms can survive freezing cold temperatures. Some frogs (like the wood frog), for example, have anti-freeze in their blood vessels! So some actually have special adaptations to survive freezing cold temperatures.

I hope this answered your question. Please ask in the comments if you want more information on this. I will gladly research up for you.