Here is a short summary. I can expand on it if you're interested.
The Weather
This was our first cruise so I can't speak to typical weather in the Caribbean in January. What I can tell you about our trip was that it was chilly! When we left Port Canaveral it was only in the mid-60's. That didn't stop the kids from going in the pool! It was windy as well. The entire trip the winds didn't drop below 15 mph.
Key West was nicer - low 70s. With the wind it made it a bit colder.
Monday at sea the sun was out and it was comfortable - mid 70s but with the breeze it was also chilly.
Tuesday - Cayman Islands were awesome! Low 80s - and even with the wind it wasn't bad at all. Sun was out - and that would be the last we saw of it!
Cozumel on Wed was terrible. If it was 70 I'd be surprised. Literally gale force winds, heavy rain and big seas. In fact by the time we left that night the cruise director came on and said that the winds from the NE the entire day had pushed the seas up to 14-18 feet and that we were in for a bumpy ride. We were indeed. You could see some of the faces of the "less-seaworthy" folk turn white.
Thu at sea was cold and windy. By Wed night they had closed the pools anyway because the seas were rocking the boat pretty good.
Fri at
Castaway Cay was again chilly - with barely a glimpse of sun. One of the cast members told me when I asked him that this was about as cold as it got for the Bahamas (mid-60s). He joked that in fact the prior week it had been 88! I didn't laugh.
Excursions
Key West
We did the Old Town Trolley on our own. In fact we didn't do anything through Disney and we made out pretty good. The trolley was fun for the kids and imformative for the adults. The drivers are for the most part very engaging and good characters. You learn a lot about the interesting history of the island. The nice thing about the trolley is that you can get on and off all day if you want. If you book it through Disney you can't.
We stopped at the Hemingway House which was very interesting if you like that sort of thing. The kids LOVED the cats. They chased them all over the grounds and we looked for the 6-toed ones. They were all very friendly and tolerant. The grounds are beautiful as well. Picked up a copy of Old Man and the Sea - and when you buy it at the Hemingway House you get a special sticker on the book denoting that fact. I am sure I paid at least $7 for that sticker.
We also stopped at the Southernmost Point - as did a LOT of people. There is a very long line you must wait in to get the classic family photo at the marker.
After that we went to the Toy Factory - which is pretty incredible if you have kids - and even if you don't. Very neat place. They have a pirate ship inside and the place is amazing. The kids eyes were as big as saucers. Just know you're not getting out of there without buying something!
Last we went to Mallory Square for sunset. A MUST. There are tons of performers, artists, vendors, etc and they put on an incredible variety of entertainment. Last time I was there in my 20's I saw the "cat guy". He puts on a show with trained cats and they do various feats and tricks. The show was the same - but the cat guy was not. I think he must have lost his medications because he truly was more insane than ever!
One thing to note - if you have first seating for dinner as we did and you go to Mallory Square - plan to miss dinner. You won't make it.
Grand Cayman
There are many excursions available through Disney and local outfits. We wanted a relaxing beach day and I had heard you could get a day pass for the Westin which is what we did. It was $40/pp and well worth it. The Westin sits on one of the nicest sections of seven mile beach and you get a room for the day, use of the lounges, the very nice pool, towels, and facilities. We rented a waverunner while there as well and had a great time. We could see farther down the beach where most of the crowds had gone - and I heard from others that it was cramped and unpleasant. Our beach was not crowded at all and then in the afternoon we sat by the pool on some NICE lounge chairs, had some drinks and food and soaked in the sun. Awesome.
Our tablemates at dinner told us they did Stingray City and the Turtle Farm and loved it. I think next time we'll give that a go for some variety.
Cozumel
Well... I'll try and be nice. Um... the people of Cozumel are quite... zesty? We left the kids on the boat and walked into town - and into the face of 30 MPH+ winds and pouring rain. It was miserable. If you don't know it already, there is a lot of shopping in Cozumel - but I'm convinced it's one large store because they all sell the same exact crap. The shopkeepers are out in force in front of the stores practically begging you to come in and buy something. It's charming for the first 10 seconds. After that it's downright annoying.
This wasn't our plan however. We had booked reservations at Nachi Cocom which we had heard great things about. It's a beach resort where you can relax, drink, go in the pools, eat, etc - all for once price. They limit the amount of guests to 100 - so it's never crowded. Of course, we never saw it. There was no way we were going with the weather we were having. Here is where I get a little peaved. You have to give them 24 hours advance notice to get SOME of your money back if you cancel. Well, with no internet you have to rely on Disney to tell you the weather for the next stop (or pay crazy prices to surf the web). They said 74 and chance of thunderstorms with NE winds of 15 MPH. Sounds like you may be able to get some beach in right? WRONG. So we didn't even go - and I have a feeling I won't be seeing any refunds in my future. I did email them to ask, but alas.... no response. They responded quickly when it was time to pay upon booking though... hmmmm.
Castaway Cay
Again - cloudy, windy, mid-60s. What's to say? We tried to make the best of it. We rented bikes and did the bike path. That was fun and it was nice to get some exercise after 6 days of gluttony. There were some brave souls who actually went in the water. I can say one thing - there were no lines for the slides! I can say though - had the weather been nicer this would have been a super fun day. There is so much to do there - but it mostly involves getting wet. Could have been a really cool day. (oh it was).
So there you have it. I'd be happy to answer any more questions or go into more detail. Hope this helps!