No. The Everglades in southern Florida would be a good example of tropical climate in America.
Texas and Florida
The name of the gulf located east of Texas west of Florida and north of southern Mexico is The Gulf of Mexico
Southern California, Southern Nevada, Much of Arizona, the southern half of New Mexico, far west Texas, southern Utah all have a hot and dry climate.
The Gulf of Mexico.
The most southern part of Texas is more southerly than the central part of Florida. Brownsville TX is almost as far south as Miami FL, but it is still a long way north of the Florida keys.
Florida is quite popular for that very reason. Southern California, Southern Nevada, Arizona, and Texas are also good locations for seniors looking for warmer weather.
The Musk turtle can be found from southern Ontario, southern Quebec, and Southern Maine to the north, south Florida, and East central Texas. Other places where they live are central Wisconsin and Minnesota.
There is no Gulf possible between the regions as you state them - Mexico is to the west of Florida and therefor there can not be a Gulf WEST of Florida AND north and southern Mexico. Your question makes no sense and thus can not be answered.
The southern states were the Confederacy. All the states from Virginia down to Texas, Florida, Mississippi etc. were in the Confederacy.
Gulf of Mexico
Gulf coast states, Florida, Texas, etc. There are ranches that have them in Texas.