Hi K.,
We try to go to the Mexican Yucutan or Mexican Riviera as they call the tourist part these days, the Cancuun, Cozumel, Playa del Carmen, Tulum areas every year.
It is warm year round and sometimes hot, the summer months you can have some rain (or the rare storm or hurricane), but in January the weather is great.
My girlfriends and I did a bachelorette cruise at the end of January a few years ago. We took a short 3-day cruise out of Galveston to Cozumel and then back. Like I said the Mexico weather was great and definitely the best day of the whole trip but on the boat deck it was windy, sunny and warmish during the day a little chilly at night, but definitely windy.
It was not comfortable for me to hang out on deck but some people did. I don't know if that is a normal January occurrence or it was just that trip, like the winds were up or something but that is the experience I had. I would check further into with the cruise people maybe. There are lots of other areas to hang out, chat, drink or read etc. but I would have rather been out in the sun. I shopped a little too much : ) but since I was on one of the smaller ships there weren't that many shops. Honestly we got a little bored but I didn't have kids yet so it could be a different story for you. Now I would enjoy just being there probably. But again it would have been better if the sun deck wouldn't have been so windy, but the evening dining was really great and we loved the day in Mexico
If you are taking the kids I would make sure your ship has lots of fun things for them to do.
If you are going to Cozumel and don't want to do any of the "pre-arranged" trips, you can get off the boat and take a cab to Play Sancho, it's a private beach with a restaurant, bar, pool, massages, waiters on the beach and they have everything you need to just relax on the beach for the day. They have snorkel gear and other stuff for kids too. http://www.mrsanchos.com/mr_sanchos/home.htm And actually your boat might arrange to go there but if not you can go on your own. I have been there a few times and really enjoy spending the day there.
My two cents. Happy traveling - it sounds soooo nice right now.