From Carnival's Ticket Contract:

8. COMPLIANCE WITH RULES, SOLICITATION, SMOKING, DRINKING, ILLEGAL ACTIVITY
(a) Guest agrees during the course of the voyage to follow the directions of the ship’s Master, or his authorized officer. Guest further agrees not to solicit anyone on the vessel for any commercial or professional purposes. Guest agrees that any violation of this Clause may subject guest to disembarkation.

(b) Guest acknowledges that Carnival’s vessels contain non-smoking sections. Guest agrees to refrain from smoking in those sections and agrees that Carnival has the right to disembark the Guest for failure to observe Carnival’s non-smoking policy.

(c) Carnival has designated the Spa stateroom and suite accommodations as an entirely smoke free environment. Guest booked in a Spa cabin agrees to strictly comply with this non-smoking policy and refrain from smoking or allowing any other Guests from smoking in the Spa cabin. Guest further acknowledges and agrees that any violation of this policy shall, in the sole discretion of Carnival, constitute a material breach of this cruise contract. In the event of such breach, Guest forfeits all rights hereunder, including the right to occupy the Spa Cabin and remain on board. Carnival reserves the right to move the Guest(s) to a non-Spa cabin or to disembark the Guest(s), at any port, as determined by Carnival. Carnival shall not be liable for any refund or other compensation or damages whatsoever to any Guest vacated from the Spa Cabin or disembarked pursuant to this provision, or who disembarks because another Guest is so disembarked, and all such Guests forfeit all rights under Carnival’s “Vacation Guarantee.” Guest and Carnival further agree that any violation of the non-smoking policy would also cause Carnival to incur damages, including but not limited to, loss of Guest goodwill, revenue, cleaning, maintenance and/or other costs. Guest and Carnival expressly acknowledge the difficulty of ascertaining the amount of such damages, and therefore agree that a reasonable estimate of the damages for any violation of the non-smoking policy is $250. Guest authorizes a charge in this amount as liquidated damages, as well as repatriation expenses (including airfare) against Guest’s on board charge account, without further notice, for any violation of the non-smoking policy.

Some other information we found online regarding Carnival's smoking policies:

Is there a smoking policy for Spa Cabins?

Smoke Free Policy - Spa Staterooms (Carnival Splendor)

Carnival Cruise Lines has designated the Spa stateroom and suite accommodations, inclusive of the balcony, as an entirely smoke free environment. Guests booked in a Spa cabin agree to strictly comply with this non-smoking policy and refrain from smoking or allowing any other Guests from smoking in the Spa cabin. To preserve Spa standards and ensure staterooms and suites are free of smoke residue, Carnival will asses a $250.00 reconditioning fee per spa stateroom or suite for guests that do not comply with the non-smoking policy. This charge will be applied to the guest's Sail and Sign account.

Spa accommodations include private access, special amenities and priority reservations at the Cloud 9 Spa. Cloud 9 Spa accommodations are non-smoking.

Where You Can Smoke: Smoking is permitted in casinos, dance clubs, piano bars and other live music venues, as well as designated areas on open decks.

Where You Can't: All dining areas are non-smoking, as are a number of public rooms, including the aft cabaret lounge, main show lounge, library, and along the promenade.

Cigar and Pipe Smoking: Ships in Carnival's Destiny and Conquest classes have cigar bars.

So, it sounds like Carnival has a smoking policy of some sort, but, from the comments I found on Cruise Critic and other online boards, they do not enforce it.  Some said the rooms reeked of smoke and others say they had no problem at all with smoke in their cabin.  Personally, we have sailed on Carnival maybe 5 or 6 times and I do not remember ever having a cabin that smelled like smoke.  Now, the casino and other areas are really bad for non-smokers and if you stay out of the casino, you may save your life and your money.....The fun and excitement of taking any of the newly published and discounted Carnival Cruises 2012 will allow for the memories to last a lifetime when you cruise the Carnival way.  For additional Carnival information regarding future cruise voyages you may want to take a look at Carnival Cruises 2013 for the next cruise season sailings for Carnival.  Other great voyages include the Caribbean so please check out Carnival Caribbean Cruises 2013 for the latest deals and specials from Carnival Cruise lines.  You may also desire some of the Carnival Mexico Cruises 2013 voyages and sailings when considering any of the warm weather Carnival cruises.  If you are thinking about any of the new Carnival Caribbean Cruises 2014 then they are now out and ready for your review and planning.  Another great place for future cruise voyage itineraries can be found at Carnival Cruises 2013 for the latest sailings and cruise information.