Cozumel does not have a bad season so much as three overlapping ones, and knowing which you have booked into matters more than the temperature. The water sits between about 78 and 86 degrees Fahrenheit all year, the air rarely drops below the low seventies even in January, and the reef is there in every month. What changes is wind, rain risk and how many ships are in port.
The Atlantic season is open from June 1 until November 30, and on Cozumel the part of it that actually costs people days is the back third, mid-August into October. Very few visitors ever see a landfall. What they see is the island version of the problem. A system still hundreds of miles out pushes swell up the channel, the harbourmaster closes the port to small craft, and the dive boats, the snorkel catamarans and often the Playa del Carmen ferry all stop together. You are on an island, and for a day or two there is no water route off it. Cozumel remembers Wilma, which stalled over the island in October 2005 and rearranged parts of the reef as well as the town. None of that is an argument for writing the late summer off. Those are the cheapest weeks of the year and most of them are fine. It is an argument for insurance bought on the same day as the flights, and a schedule with slack in it.
Norte season is the one nobody tells you about. From roughly November through March, cold fronts push down from the north and bring hard north winds. The harbourmaster closes the port to small boats and sometimes to the Playa del Carmen ferry, which cancels dive trips, snorkel boats and catamarans for a day or two at a time. Nighttime temperatures can fall into the sixties and daytime highs into the seventies. Nortes are why every experienced diver books a Cozumel trip with a spare day at the end.
The cruise calendar is the third season, and it works on a daily rather than monthly cycle. Cozumel is among the busiest cruise ports on earth, with three piers that can take four or more ships at once, and the difference between a four-ship Wednesday and a one-ship Sunday is felt everywhere: at Chankanaab, on the shallow reefs, at the beach clubs, in the taxi queue and along the downtown blocks. Peak ship traffic runs roughly December through April. If you are staying on the island, look up the daily ship schedule before you choose which day to do Palancar or Punta Sur. That single habit improves a Cozumel week more than picking the right month.
If you want a short answer: February and March for diving, when visibility peaks around 120 to 130 feet, the water is a crisp 78 degrees and eagle rays work the deep walls at Santa Rosa and Punta Sur. Late April into early June for the best all-round balance, once the nortes have finished and before the heaviest rain and heat arrive, with hotel rates easing and the ships thinning out. September and October if price is the priority and you are willing to accept genuine hurricane risk and softer visibility around 75 feet. July and August are hot, humid and busy with families, with the warmest water of the year at 84 to 86 degrees and afternoon downpours most days.
One comparative fact worth carrying: sargassum, the seaweed that lands on the Riviera Maya's mainland beaches in spring and summer, affects Cozumel's west coast far less, because the island shelters its own leeward shore. The east coast catches what the open sea brings. On a bad sargassum year the mainland and Cozumel are not the same holiday at all.