Nitrox $10 per tank in Cozumel. You're right that the diver volumes up there are much higher than in Belize, which probably helps to explain why people can make fortunes running dive centers in the Yucatan whilst most operators in Belize barely get by. Dive prices are nominally the same as well ($30 for a local dive), with discounts easier to get in Belize. Just because people are desperate for business.
By late Jan the water is beginning to warm up, but will probably still only be 81-82F. Air temperatures can be relatively quite cool, and some lightweight long pants and a sweatshirt or light fleece are certainly in order. Can't give a temperature, but a lot has to do with windchill. I dive with a lycra/nylon skin year-round, and only rarely feel underwater that I could do with a bit more. A well fitting 3mm full suit should be finehere for any season for all except the most warm blooded of people. I do know of one person who uses a drysuit in winter, and he and I have dived together - he in his drysuit, me with my skin. I carry a very large nylon raintop on the boat for night dives, because although I'm not usually at all cold under water it can be freezing cold at speed in an open boat. One reason we installed hot showers at the dive center, and take hot cocoa for immediately after the dive.
I see Don corrected his statement that nitrox was much cheaper in Mexico, but the principle he raised remains. Whether or not something is "daylight robbery" depends what it costs to provide. Costs in Belize are unbelievably high and rising all the time, and providing anything like a quality dive product for $30 per local dive is now very difficult. Many people say they hate cattle boats, but they don't seem to appreciate that the cost of operating a boat is independent of the number of divers on board, so the fewer the divers the more that must be charged each. I dived in Cozumel last summer, and was unable to find anyone prepared to take me out for less than $30. And I saw no boats with fewer than 20 divers. In Belize, at any rate at my shop, we rarely go out with more than 6, and often 4 or fewer, and often discount dives by 20% or 30%. Just work out the economics. Gasoline here now costs over $5:50 per gallon.
I should have said that Belize gets very windy in the spring, and the cool wind can be quite debilitating. Nominally that's in March, but the climate seems to be all over the place these days so even in January I'd bring what I said above, plus something windproof. It's still very humid, though, so breathability is crucial. The wind can churn up the sea a lot, and a couple of years ago we had many divers wanting to go out, but couldn't even attempt to go through the barrier reef to the dive sites for a full two weeks. Boats have been known to overturn in the reef opening, so we take these weather conditions very seriously.