Welcome to CA. I hope you enjoy FF. I have stayed there many times. Its quite a nice park and in a beautiful area. Before you settle in, check out Lake Cachuma, about 15 miles east of FF, through Solvang. Also a nice little rural park, with rates quite a bit less than FF.
Anyway, getting back to your post and from professional experience. CA Driving and Registration requirements are that you must have a CA DL and change of vehicle registration with 10 days of taking up residency (though without checking it may be 15 days for registration). Residency can be having mail delivered, working, residing in a shelter where utilities are paid by you in your name. From how you describe your situation, legally you would be required to obtain a CA DL and re-register your vehicle(s).
Typically this only becomes an issue if you get stopped by law enforcement, after the aforementioned period. If you haven't changed over, you may well be cited for not having a current CA license and veh. registration. Usually that prompts the violator to obtain the necessary before the court date and often the ticket is dismissed - but not always. It depends largely upon the jurisdiction where the ticket was issued and circumstances surrounding the original issuance. There are a variety of circumstances which might cause an officer to request your DL and registration - one of which may be simply driving around with Florida tags on the vehicle, even though they may be valid (in Florida). Now if you were stopped by an officer, say within a few weeks of your arrival, you may be simply 'advised'. However, if it is a month or two or longer and, through converstaion, you identify your local mailing or business address, a citation is likely. OTH you are less likely to be stopped while driving a MH with out of state tags, but a car or truck is a different matter. Of course you have little control if involved in a accident and the police attend the scene...the truth will out. It's not a big deal to change over but time, fees and a visit to DMV are involved. (make an appointment on line, it's much less hassle).
You should also check, and perhaps change, your insurance policy to reflect any new address. The rates and coverages may be different. Insurance information and current registration are required to be carried in the vehicle at all times, while on the highway. Furthermore, CA law does not permit you to have more than one DL so having both Florida and CA is not legally an option, though there may be ways to circumvent that requirement. Your voting rights will not necessarily change.
Also, from a practical point of view, many business will not accept 'out of state' DLs for identification purposes, if you find it necessary to produce ID.
Again, welcome aboard and to CA.
BT