Yes, you can smoke in your cabins. Just please do not open your cabin door and allow it to come out into the hallways.
I can understand why you would think the cabins are nonsmoking. Carnival goes to great lengths to post the "designated smoking areas" (not public...not private...just all "designated smoking areas) in the Capers every day. This indicates where it is ok to smoke. You will never see the cabins or balconies listed. Also, you will never find an ashtray in the cabin or on the balcony.
Personally, I think Carnival does this to try to avoid any legal responsibility should a fire occur in a cabin from an unattended cigarette. I don't think it would work, but Carnival's legal position would be that they are not responsible because the "cabin" was not listed as a designated smoking area.
Have a great cruise!!!