Certainly.
I voted last November for the Minnehaha Creek Watershed Board (where I live), and then early this year got a mail ballot to vote for a director of the water & drain tile board from a rural county (where I grew up, and still own farmland).
The first probably happened because many states update their voter database via the Post Office’s National Change of Address system (just like many businesses do). The second happened because the state can’t assume this just because your mailing address is different from your voting address. They are different for lots of people: those with PO Box or Rural Route mail delivery, for students who go off to college, people serving in the armed forces, or people who spend part of the year elsewhere (here in Minnesota, we have many seniors who spend the winter in southern states). The state can’t arbitrarily deny people their right to vote for these reasons.
This happens all the time with politicians, of both Democrat and Republican persuasions. If I am not mistaken, Hillary Clinton was registered in Arkansas when she was elected in New York. There have been Republicans who have had the same thing happen (Quayle?). It seems rather common for congresspeople. I guess they have so many pressures, they forget.
You’ll see this every so many years in the news. It never comes to anything, since the guilty party always says it was just an oversight and, since they only voted once, no harm - no foul.
I don’t see you having a problem, but why register to vote in Florida if you don’t plan on voting there? Voter registration is not a requirement for residency.
excavating (for a mind)
**PRR **- if you do decide to move down here…let us know what part of Florida. There are (apparently) a few of us Dopers in the area.
Don’t get too excited. By the time they get around to counting your vote, the election will be over. 
In some cases, you can get votes based on the area of property you own or even its value.
I keep forgetting this. Here in Canada, federal elections are run by Elections Canada, which is responsible to the federal parliament; provincial elections are run (in my case, anyways) by Elections Ontario, responsible to the provincial parliament; and municipal elections are run by the municipalities. Completely-different groups, completely-different ballots, completely-different days.
These groups are also responsible for drawing the boundaries of their electoral districts (“riding”). In Ontario’s case, Elections Ontario simply decided that their ridings would be the same as the federal ones, and (at least the last time I voted in a City of Toronto election), the Toronto districts were each half of a provincial riding.