Hi, it could be a cherry tree (any blossoms?), but without more info. or a close-up of a few leaves, it's hard to say.
I live on the west coast of Florida and went to visit a friend on the east coast, where I saw this tree. I've never seen anything like it. The bark is like skin and peels like sunburned skin. There were a lot of initials carved into the tree and I happened to notice that some of the initials were lifted at the edges, sort of like a scabbed over wound, so I stuck my fingernail under one and it lifted right off. The tree was healing itself quite nicely. I tree is so beautitful that I posted on another forum and everyone is asking me what kind of tree it is and, alas, I don't have a clue. I'm sorry I didn't take more pictures of it, but I do have one that is closer - I don't know if it would show the details needed for identification. The bark is so unusual, I was hoping someone would be able to identify it by that.
I'm not familiar with it, but I'm thinking Bursera simaruba, or the gumbo limbo tree. Here's an image search for "gumbo limbo" and an information sheet (PDF) on Bursera simaruba for your consideration.
The colour, open growth form and peeling red, skin-like bark are suggestive of our native arbutus on the south west coast of BC. I've never been to your area, however, and am not sure if a relative of this tree would grow there. Our arbutus trees tend to be taller and narrower in form than this, but the bark certainly sounds the same. The arbutus leaves are leathery and evergreen. I can't tell from the photo what the leaves are like on your tree. Anybody out there know if there are arbutus trees in Florida?
I called my friend on the other coast and she picked up her uncle, who is a botanist, and drove him to the park to see the tree. He said it's a Gumbo Limbo tree. Thanks for the responses. What a great site!
Daniel, I do believe that you correctly identified this beautiful tree, all parts of which are poisonous and which is native to south Florida and the tropical offshore islands. I read that the Glades Indians captured small birds by the ancient method of using bird-lime: they boiled the glue-like sap of this tree with water then spread it on favored branches, where any small bird landing became stuck. They then ate, sold, or bartered the birds. It seems to me that this particular specimen would be a favored tree for children who love to climb trees.