Originally settled by the Olmec before even the Maya, Cozumel has been inhabited for millenia. Its original inhabitants and many of their sacred temples were destroyed by Hernan Cortes and smallpox in the 16th century, though some ruins do remain visible on the island today. Maya women would come to Cozumel to worship the fertility/moon goddess, Ix Chel, traveling by canoe from Playa del Carmen or Tulum in a fashion similar to many of today's visitors. The Maya also gave the island its name: 'cuzam' means "swallow" like the bird, and 'lumil' means "land of." So Cozumel, to the Maya, was the Land of Swallows. Indeed, the island is famous for its biodiversity. There are a handful of endemic species (animals found nowhere else on earth) including a raccoon, a fox, and a colorful species of toadfish. Some of these species may already be extinct though, as frequent hurricanes the past few years have taken their toll on the local landscape, reefs, and wildlife.
Cozumel is prone to hurricanes, though they're not frequent by any means. Lying just south of the Tropic of Cancer, the weather is warm and obviously tropical, with a prolonged wet season. It's proximity to the ocean also makes it pretty humid, around 80% on average. You're definitely not going to have to worry about freezing while staying in this jungle paradise!
Cozumel is a well-known gay friendly area of Mexico. In fact, same-sex marriages are legally performed in the state of Quintana Roo to which Cozumel belongs. There is an annual Pride celebration on the island, and there have been several hotels or bars in the past that have advertised to a gay clientele. The island's population is small though, with only about 100,000 people; so it seems like long-term, sustainable, gay-specific venues would be dependent on an influx of gay residents or a significant continuing gay tourism pattern. That said, there are plenty of bars and resorts on the island you will feel completely welcomed at. People in Cozumel seem to be enjoying their island paradise too much to worry about it really.