Will the engine be ruined if there is no antifreeze in cold weather?

Yes. The danger is, that when water freezes it expands, when it turns to ice. The coolant galleries inside the engine block may suffer cracking, if there is no where for the ice to expand to. You may be lucky and the core plugs will blow out instead. (Still a lot of work to put right).

Antifreeze lowers the point of freezing and prevents this expansion problem.