I can't give you any specific advice about the areas you are interested in, but having spent some winters in southern RV parks I want to assure you that what you are planning is very commonly done. By the way, the park we stayed in last January-February, Tampa East RV Resort, is 80-90% filled with French speaking Canadians from Quebec, meaning that us Anglophones were in a distinct minority!
Many southern RV parks offer storage services. You will want to get local advice on "summerizing" your trailer for storage in the hot summer season--e.g. bug and rodent protection, etc.
Yes, it is common for long-term-stay RV parks to charge for electricity in addition to the site rental. Typically there is a meter at each site. As I recall it never cost us more than $20 - 30 a month.
See you down the road,