It is popular with many, especially locals, to view the dawn of the new year on Cozumels East coast. It is said that first rays of sun to bathe the country , are at this location(although that is disputed by Isla Mujeres).
Cozumel officials have announced checkpoints will be set up to assure no alcoholic beverages are taken to the beaches at that time. I would doubt they can be totally successful but they will try.
They will also be using the breathalyzer in the cross island road and the South hotel zone of the island.
If drinking for the New Years Eve festivities, let someone else drive.