In addition to what jd posted, there are lots of Cozumel residents and divers who discourage ordering or fishing for grouper at anytime of the year. Although I love it, I do try to avoid it.
That said, these are the "closed" seasons for Quintana Roo:
Conch May 1 - Oct 1
Octopus Dec 15 - July 31
Lobster March 1 - June 30
Grouper Feb 15 - March 15
If you just have to have it, please refrain from fishing for it during the closed dates, and also refrain from ordering it if you see it on local menus. If it's on the menu during the closed season, don't be shy about asking where it's from and/or if it's been frozen. Why pay for shipped in and/or frozen seafood when you're on an island? You can do that at home anytime.
As far as I know there are no seasons for snapper (and fyi, Casa Denis does a great one grilled w/ garlic). Any shrimp I've had in Cozumel or on the mainland has been from the Gulf.
It's getting tough to be a seafood consumer. On one hand we're told that eating fish is good for us, and on the other, if you have any interest in ocean conservation, the lists of what not to buy seem to keep growing. In my area it's close to impossible to find things that I feel good about buying. Just isn't available in the regular stores and/or at prices the average person can afford.
I make up for it on vacation, that's for sure.
