This sounds like lots of fun to follow, and Ken, way to go on building a piece of Florida onto your Mississippi home! That's going to be easier and cheaper in the long run than moving down here, I'll bet. (be sure the mini-split they put in has heat as well as a/c capability, btw)
Kathy, I'd also recommend a mini-split system for heat and a/c in your new greenhouse. They're super efficient, can use just the fan when needed for air movement, quiet and best of all they're inexpensive and very simple to install, as well. We had one put into our bedroom so that we could keep it cooler at night than the rest of the house (for certain women of a certain age who get too hot at night . . . )
Rather than kicking on and off, and throwing a hurricane of frigid air like a regular a/c unit does, the mini-split runs at a constant low speed and keeps the temperature from bouncing up and down. Good for growing orchids and other tender plants.
When you think about the cost of extending vents etc. into the new greenhouse from the house system, I'll bet it would be comparable to putting in a mini-split, and the mini-split would be SO much better. You'd be able to control the temp in the greenhouse separately from the house.
