Mimi, yes smoking is permitted in the cabins. The dining room and show theatre it is not permitted. Also, one side of the ship allows smoking and I think it may be the port side but not certain.
And nothing worse than not being able to enjoy your balcony because the next cabin (upwind) is smoking all the time on their balcony and the smoke blows into yours. I sincerely wish that they would make the cabins on one side of the ship non-smoking. We lost the use of our balcony for an entire Alascan cruise because of a constant cigar smoker in the next balcony. I hope he had a wonderful time because we certainly didn't.