I'm the family cruise editor here. According to all the articles I've read in my trade publications, by the afternoon of the first full day at sea, it should be warm enough to use the outdoor facilities, accdg. to NCL. This ship has a great water play area for little ones. We were on its sistership in Hawaii and my two year old loved the water play area. NCL is one of the few lines which takes kids as young as two in their youth program ,so that should work well for you. I'd love to hear how it goes.
Luisa Frey Gaynor