Disney states in their documents package that personal coolers are not allowed. So, if you show up with a hardsided cooler you may have a problem. they definately will not let you take anything onboard that already has ice in it.
That said....many people, including myself do bring a small collapsible cooler (holds about 6-8 cans) that I pack in my checked luggage. If I am bringing on my own alcohol I will pack it in my carryons and just get ice later from my room steward if needed.
I have not heard of
DCL limiting how much alcohol you bring onboard but I think discreet is always best....I would not try to carry on a case of beer....mainly because you will have to lug it around until your room is ready.
Some people have reported that they were able to check cases of soda/water with a porter at DCL but do not know if that is still allowed or if it would work with alcohol.
Another note...any alcohol you bring onboard yourself either at Port Canaveral or any of the other ports you are allowed to consume onboard.....however, if you purchase alcohol from the duty free shop onboard DCL will hold that purchase for you until the end of the cruise and then give it to you. You are probably better off just bringing a small amount of alcohol onboard at PC and then purchasing more if you need it on the islands...it is much cheaper.
No opened bottles are allowed off the ship when you return so either drink it all or leave it for your room steward. There is also a limit as to how many bottles each person can take off the ship that were purchased in ports/onboard to bring back into the country...not sure what that amount is.
Another suggestion is to pack various sizes of zip lock bags....they are great for packing ice in to put in a small collapsible cooler if you wanted to bring it up by the pool or to the beach.
MJ