Can I buy a house in a short term rental area in Florida and live in it all year round?

You most certainly can, there are some terrific communities zoned short term that have owner occupants and/or long term tenants. It's a nice feature to have as when you sell you are opening yourself up to more buyers on an international level. And if you ever decide to move and don't want to sell you're home you have the option of renting long term as well as short term.