This was 5 years ago and one year ago, so it's not pre-revolutionary nostalgia. I might be wrong on how well it worked inland, but I remember feeling cool no matter which city I traveled to.
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.
Brudgers makes a good point about the thermal capacitance of masonry below. If you spent much time in old, stone/brick/masonry buildings, they'll feel significantly cooler.
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.
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.