Disney allows you to bring on a certain amount of beer and wine, that you're free to enjoy in your stateroom. You may board the ship with 2 bottles of unopened wine or champagne (normal size, don't go crazy) or a 6 pack of beer (12 ounces), to be brought on board in your carry on bag. You may also bring the same quantities on at each port. Staterooms have small refrigerators, so keeping things cold is not an issue, and if you would like some ice, your room steward will bring you some.
For such a family friendly atmosphere, there are a lot of places to buy alcohol. There are bars on the pool deck in both the family and adult sections. Bars by the main show theater, and bars in the lounge areas. You can also order a drink at meals. Another tip! Gratuities are added with each drink purchase automatically. Pay attention when you sign the slip authorizing the drink charge...it's there, but there is also a line to add a gratuity. If you'd like to add an additional gratuity that's great, but be aware that you are double tipping.