Cozumel has a long list of things laid on for people who arrive by ship. These two are not among them, and that is the point.
Carnaval
Cozumel's Carnaval is among the oldest and best attended in Mexico, and it is a community festival rather than a tourist product. Comparsas — neighbourhood troupes who rehearse for months — parade along the malecón across several consecutive nights, with costumes made locally, a Carnaval court, and a crowd that is overwhelmingly islanders.
When it falls: the days leading up to Ash Wednesday, which moves with the church calendar. Ash Wednesday falls on 10 February 2027, which places the 2027 celebration in the first half of February. Confirm the exact parade nights with the municipality closer to the time, because the programme is published locally and the route and hours vary year to year.
If you are here for it: accommodation in San Miguel tightens noticeably. Book early, expect the malecón and the streets behind it to close to traffic in the evenings, and do not plan to drive anywhere in town after dark on a parade night. Watch from the street rather than from a reserved area you did not pay for, and let the comparsas through.
Día de Muertos
31 October to 2 November, fixed. Observed here as it is across Mexico: altars — ofrendas — built at home and in public buildings, marigolds, photographs of the dead, the food and drink they liked, and families spending time at the cemetery.
It is not Halloween and it is not a parade laid on for visitors. The mood is warm rather than sombre, but it is a family occasion with real grief inside it.
How to be a good guest: look at public altars, which are built to be seen and are often genuinely beautiful. Do not photograph families at graves. Do not treat the cemetery as a photo location. If you are invited to look at something, accept graciously; if you are not, do not intrude. Several restaurants and bakeries make pan de muerto in the days around it, which is the easiest and most welcome way in.
The third one, for completeness
The El Cedral fair, around the end of April and the start of May, is the island's oldest celebration, held in the inland village at the site of Cozumel's earliest settlement. Rodeo, music, food stalls and a religious procession, almost entirely local. Confirm dates locally in the year you travel.