Florida is similar to Cuba. If you own a home located close to the beach, you're in good shape. You can leave your windows open all winter, and most of the fall and spring. As you move inland you lose the ocean breeze cooling effect very, very quickly though.
I grew up in a turn of the century bungalow home about 3 miles from the beach on the east coast of Florida. The home was built, and lived in, by a contractor who developed much of my home town in the 1900-1915 time period. The homes had many windows with long-ish eaves (for shade) so you could take advantage of the breeze. Back in the early 1900s, that was the only option you had.
Growing up, we only had a window unit air conditioner, and my parents couldn't afford to run it much, so I can personally attest to the difficulties associated with living in South Florida with no air-conditioning. It was never "quite cool" (by air-conditioned standards) in our house during the summer, even though the home was designed specifically for the environment. For most of the day it stayed cooler than it was outside, but on a cloud-free summer day, there was no relief, inside or out.
I'm not saying we shouldn't use innovative techniques to reduce energy usage, but I am contesting the idea that you can build an above-ground zero-energy home in Florida.
This was October to May, so like I said, the system may break down in summer. It was still warm through those months compared to what I know in Canada, but I know summer is warmer still.
Unfortunately, you correctly observed that October through May is an entirely different animal in this region. All the windows in our home are open currently. We get many opportunities like this through the end of February, tapering off through March and April. By May, things in Florida start to heat up. Most could manage it, but I wouldn't call it comfortable.
In June through September, you can sit on your porch at 10 PM and sweat will stream down your face due to the heat and humidity. It is an insufferable burden to go without air-conditioning in this place during the summer months.
I also suspect that Cuba, being such a narrow strip, and having significant elevations in areas, has a more temperate climate than flat, hot, and wet Florida.
I have no idea how they did it. This was mostly in coastal areas, so there was much wind. But it even worked in inland areas. The windows did not let in much light. There was usually no air conditioning, and inside was generally much cooler than outside.
In any modern buildings, air conditioning was required. I also expect this system might not have held up in the warmest summer months.