The small cooler comments in the Carnival FAQ are for non-alcoholic beverages. The wine you can pack in your suitcase or carry-on (if you are not flying in).
Large cooler restrictions:
Carnival Cruise Lines does not allow guests to bring large coolers on board its ships. However for purposes of housing small, personal-sized coolers no larger than 12” x 12” x 12” for the purpose of housing small quantities of non-alcoholic beverages and/or medications are permitted as carry-on luggage. Screening and movement of large coolers through embarkation is an impediment to the boarding and security screening process. Therefore, large coolers are not permitted as carry-on or checked luggage.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Alaska 2014 - haven't picked a cruise yet
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, Caribbean 2013