Is there a word that means "frozen to the point of being damaged beyond repair"? I am thinking of organic things, but I would also like to find a word that can be used generally for non-organic things also like hardware, but if you can't find a general word it's ok.
Generally, the nature of the damage is specified, rather than the cause. The answer by Jasper mentions "burst pipe", which is a common phrase used when a pipe freezes and is damaged, but a pipe can burst from reasons other than cold -- excessive pressure, which is more likely to come from heat than cold.
The boiler overheated, and the pipes burst as a result.
A board, or a sheet of metal, or a concrete slab, may crack from cold, but such things might also crack from an impact, say the blow of a hammer. A glass might shatter or simply break from the action of freezing water, but again those verbs can be used with other causes. "frostbite" is specific to cold, but it is a very specific type of injury. It can also be used for plants, and for injuries that can and do heal.
For an animal or human, one can say "froze to death" which is surely beyond repair. One might say that a plant has been frost-killed. Any living being may suffer hypothermia -- injury due to cold.
In places that have cold winters, the phrases "burst pipe" or "burst pipes" or the words "pipe burst" or "pipes burst" in a sentence usually mean "pipe(s) froze beyond repair, due to a combination of cold weather, the pipe was in an unheated location, there was water in the pipe, and there was not a trickle of water through the pipe." These phrases are usually preceded by a determiner.
For humans and other animals, saying the person or creature suffered from "frostbite" means that a (possibly tiny) part of the person or creature was frozen beyond repair.