We just returned from the Dream NYE sailing. December 29, 2013 - January 2, 2014. The answer to your question "do they do anything special?" YES!!! It was worth every penny, in our opinion, for the NYE sailing. They had a special menu in the sit down restaurants for NYE, they gave out complimentary glasses of champagne and they had
Disney Cruise Line, Happy New Year 2014 on them (glasses were a heavy duty plastic, we kept them as souvenirs), when we got out of the show that evening in the Walt Disney Theater, they were giving out hats, tiaras, and beads, noisemakers, upon returning to our cabins we had Don "Ducky" Williams 2014 lithographs with the Disney characters and a box of
Disney Cruise Line truffles that had Happy New Year on the box, they moved the fireworks to NYE instead of Pirate night, the NYE deck party was insane and we felt like we were in Times Square it was so much fun. The Aqua Duck was all lit up and the music was fun, it was great to see all the families having fun together and the countdown was Disney magic at its finest! Many of the FE gifts we received were NYE theme so that was fun too. We'd also brought our own noisemakers. Don't hesitate, book it.