Check out the listings and reservation calendars of TV homes on ****.com (vacation rentals by owner), to get an idea of how rentable they are. I just looked at the calendars of about 20 listings, and almost all were booked for Nov. and Jan. thru April.
There is demand, also, for one-month rentals in the winter, because most owners prefer and get a 3-month renter for JanFebMar. Finding a one-month rental in that time frame can seem almost impossible, and one might have to wait for a cancellation to show up in the ads online and in the Daily Sun.
See:
http://www.****.com/vacation-rentals...o/the-villages