I feel like I should probably respond to my post here so I don't leave anybody hanging.
In the two weeks I was there, I didn't find a nude beach. What I was told by one local is that the east side of the island is a bit dangerous for swimming. One person I meet at the hostel I stayed in on the island told me he went skinny dipping on the beach over at Playa del Carmen but that was around midnight.
Also a lot of drugs comes through Cozumel on the east side so there's a lot of military/police patrol too.
If you want to find a nude beach, I would look somewhere along the mainland. (Tulum supposedly has nude beaches).