Eagle flies to about 5 airports down there. Havana, Gitmo, Camaguey, Holguin and (I wanna say Cienfuegos?). I've been down there as an FO. They are special flights for Cuban nationals or former Cuban nationals. They can only go if they left the country properly. We took one guy down there and they wouldn't let him in, had to take him back with us. Apparently he had taken the hard way out (inner tube or a 56 Chevy with 55 gallon drums welded to it maybe?) and there is no coming back for those people. I believe we can also take down people who are approved by the state dept as well as government/military people.
Usually a full cargo hold on the way down, people wearing multiple layers of clothes (for family). Coming back the cargo hold usually is empty.
There is the heavy military presence. There are surface to air missiles about 100 yards off the runway at Holguin, under that camo netting stuff. Tanks, helicopters, you name it. They're ready (for what I don't know). Its pretty cool though. There is a big sign at the airport that says, "Socialismo o muerte" -- socialism or death. Nobody seems to be smiling much, especially at us Americans.
We are not supposed to leave the 'shadow' of the airplane. You don't stay there very long. Nothing breaks (there is NO maintenance there - at least we don't want to find out). ATC takes forever to respond when you call them - at least for us - I think they were playing dominoes. Some restricted areas they don't want you near, other unmarked areas they don't want you near. Other than that it's business as usual. Its actually kind of fun to go down there. I'd like to do a Havana trip someday.
But yep, we can do it. Its just done under some special government program and they are usually considered charter flights.