X-mas is really celebrated in Mexico on X-mas eve. I'm a bit bummed about having to fly out on X-mas eve as it is like the one time of the year the island says to heck with the tourists, this is our time, and $ and business will just have to wait. Parties run late into the night and early morning and fireworks can be heard into the wee hours (no, they're not gun shots). You'll find most everything will close mid to late afternoon on X-mas eve. There will be a few restaurants still open but very few. If I recall Casa Cuzamil in-town has been open X-mas eve the past few trips. X-mas day most everything in-town is closed in the morning but opens mid to late afternoon. Dive ops may not offer afternoon trips on X-mas eve but on X-mas day my dive op is up and running its regular schedule as it's peak season, the boats are full, and there is money to be gladly made by all.
Also.. NOTHING stops the unrelenting arrival of cruise ships (not even X-mas). With port closures due to the hurricanes hitting other popular cruise ship ports in the Caribbean I expect Cozumel's ports will be at maximum capacity every day throughout the season.