Fresh and cooked Oysters can be frozen but we should keep a couple of things in mind. First, freezing should always be done in an appropriate airtight freezer container. You should label the contents with the date you put them in the freezer. If you freeze fresh oysters, they should not be eaten raw once they have defrosted. You should also not refreeze oysters (fresh or cooked) once they have defrosted. Defrosted fresh oysters can be used in cooked dishes with no problem. Freezing may affect the texture of the oysters but the flavor should be fine.