Generally, the nature of the dame 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 slap, 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.