Adding climate control to the lanai

I’d really like it if my lanai had some form of climate control. I lucked out with having a huge attached lanai to my home. The windows are all screens so I can get a fresh breeze in. Originally there was a ceiling fan in the space. The problem is that I like to work out in the lanai and the fan got in the way. Taking down that fan was great and awful. I now only have the breeze coming through screens as cooling. I have no form of heating either. So working out on the lanai all year around is not feasible right now. In the winter I bundle right up and freeze to death. In the summer I basically sweat buckets the whole time. I have been thinking about changing out the screens with actual windows. Then I would add a ductless mini split to the space. I would not need a real big one either. The lanai is not all that large. I also would hardly need to use the ductless HVAC, just an hour a day. Most days I could get by with nothing. I could open the windows and use the breeze. On cold winter days a little heating would be great. Sometimes in the summer, the sunshine is pouring in. I would like some AC to combat the hot sun. We shall see through. I first need to talk to an HVAC specialist to see if ductless HVAC installation is possible for my space. I really hope it is though. I would like temperature control.