Yeah people keep their RVs in Florida year around. RV owners can pay for storage at some parks during the summer months or at a storage facility nearby. I've been told that there are services that provide moving to and from storage to your site at a specific park. I know several people in our park, Rock Crusher Canyon in Crystal River, FL, that do exactly what you've mentioned doing.
You need to check with parks in your geographic areas of interest. In some cases older RVs may not be allowed, although there are plenty of parks that will allow well taken care of units.
Obviously you'll need to find someone to tow your 5th wheel down if this is what you want to do. Good luck!