Awesome, fast response from HAL. Yes, you can bring your own drinks, just not beer/liqour. See reply below:
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.