The UF vegetable gardening guide says last plant date is March, but I'd think if you do it immediately, you'll probably be o.k., since it was cool for so long.

Here is a link that might be useful: Florida Vegetable Gardening Guide

The UF site should have culture info for you as well. I know melons can be heavy feeders, so if you're doing it organically,composted manure might be a good amendment. You might find a local stable that would be happy to give you some for free.

I just started my Winter squash seed - also slightly outside the window in the gardening guide, but I always manage to fudge by a week or so on those planting dates.

Barn stall litter is an ok mulch in modest amounts. Pine shavings plus some urine and the actual manure is primarily coarse fibers passed through the tract undigested. It is overall of very limited value as fertilizer almost all of which is the urine. It is way too much wood, and wood, even softwoods are not the thing to be adding to sand soils. There will be some trace minerals from the additives to the feed, which could be viewed as free minerals, but if large amounts are used chronically could even overload some minerals not to mention far to much bulk carbon as wood shavings.

Composted hay will be better if you can find some rotted round bales. Then there is the mushroom plant in zellwood where you can pick up spent mushroom bedding. it is pretty good stuff, and a good base OM to add mineral salts to, like standard veggie NPK chemical fertilizer. If you add salt fertilizers to sand soil without adding OM you will burn out the tiny native residential OM and render it completely worthless for the next season. You could even use the barn stall litter to buffer chemical fertilizer, much better than nothing.