Yes, it should be possible for you to register and insure a vehicle to keep at your vacation home in Florida. There are many "snowbirds" that live part of the year in Florida and the other part in a different part of the US or even out of the country.
Florida requires any part-time or seasonal resident living in FL for 90 days or more during the year to obtain a Florida personal injury protection (PIP) and property damage liability (PDL) auto insurance for their vehicle. Since it sounds as if your vehicle will remain in Florida year round then you will need to keep this FL minimum insurance on the car for the whole year.
For the months that you are not in Florida you must continue to maintain insurance on your vehicle or surrender your Florida tag and registration at the nearest driver license or tag office. If you choose to do this, when you next return to Florida you can register the vehicle after you have obtained proof of FL insurance once again.
To get information on how to register a car in Florida, contact the FL Department of Highway Safety and Motor Vehicles (HSMV). Click here for an insurance quote for the vehicle you purchase for your vacation home in Florida.