While a material is wet there can be damage due to freezing. But  due to the moisture a material can also get weak or funerable to other damage mechnisms

Example of freezing damage to masonty: On left the mortar has completely desintegrated
while on the right the point mortar has come out

An example of freezing damage to extruded fired clay brick

As a coating is failing moisture will penetrate and the wood will start to rot