Due East of Winter Haven, on the other side of Lake Kissimmee is the Bull Creek Wildlife Management Area. I grew up hunting deer and hogs there.
I agree with Doyle... Leases are expensive. Getting permission to hunt private property is about as difficult as passing a kidney stone...
The quota system Doyle was mentioning... read up on the current rules, as I've been out of FL for 19 years, but the first week of each season was restricted in each WMA. That week was broken up into 3 periods: first weekend, Mon-Wed, Thurs-Sun. You applied by a cutoff date each year for quota permits for the seasons you want (rifle, muzzleloader, bow). You could only get drawn for 1 in each season, but the permits were transferable with a restriction that they could not be sold... If you knew who to talk to, you could get permits... Only so many permits were issued for each WMA for each season, so it narrowed down the field quite a bit. Where I hunted, I rarely saw other hunters in the field.
Public land hunting on weekends (after quota) was an exercise in futility and could be dangerous. The friends I used to hunt with quit going after seeing vehicles shot up, tree stands stolen, people sitting in their tree stands, etc. Since you are going there to retire, you could probably take advantage of the weekdays when most people are working, especially late season when most folks have forgotten about hunting and are turning their attention to flats/bass fishing. Climbers work really well on the cabbage palm and pine trees. Use hang-ons for the oak trees and take the steps with you. I would not use ladders, as we always had a few stolen every season.
There is some good duck hunting to be done down there as well: bluewing, greenwing, cinnamon teal, widgeon, pintail, ringbill, mottled ducks. Highly recommend a boat, as the fishing opportunities are great as well!