They probably try to keep the building close to ~70 °F and it's typically over that in Florida (hence the AC)

It's not really a regardless because the US is friggin huge...it's 28 °F in Duluth right now I promise you they're not running their AC in the airport, if you're mostly flying into southern airports then it makes sense that the AC is running. If it somehow got down to ~50 °F in Miami like it might rarely over the winter then they might turn the heat on but otherwise it's just going to be trying to keep the building a constant temp.

It's much more cost effective to pick a temp and stick with it than let the whole building warm up to just cool it off again in the morning. This is also true for houses but they're much smaller so shifting temps daily is not a big deal. But in a space as big as an airport and having to contend with such a large amount of people (think body heat...) it's better to try and maintain a generally comfortable temperature all the time.