Ourlife had asked Holland America about drinks and here is the response "
Thank you for your recent correspondence with Holland America Line regarding bringing beverages on board your February 3, 2013 ms Nieuw Amsterdam cruise. Beverages such as soda, juice, and water may be brought on board as long as the guest carries it themselves for in-room consumption.Please note that if you are drinking a beverage carried on board in a public venue you will be asked to return it to your stateroom."
Sleddog has said that she does give her wine to the porters with a luggage tag on it and a nice tip to ensure it makes it to her room with no prob. On the HA trips we have taken, we just carried our case of wine and champagne on board with us with no problems. I'm going to try to give it to the porter this time though.
Another couple of words of advice, take a large mug with you to put your "beverages" in and you will not have problems drinking what you have brought on board outside of your stateroom. Lastly, there is a $15 corkage fee if you bring a bottle of wine with you to the table. So if you are only going to have 1 glass, fill it in your room and bring it to dinner to save some cash.
You can wear anything you like at dinner. There will be at least 1 formal night but not sure how strict it is on dress-code as we usually skip that dinner and eat at the buffet since we are casual too.