I did a unheated greenhouse last year and had success here in Pensacola. Lychees, Ross sapote, mango, white sapote, and avocado. The only time I was really concerned was when it hit 27F and I put the mangos in the garage. I was too chicken
The Ross sapote was the only one that got burned a couple of times when it got around 29 outside/32 inside. This year it is fruiting so no worries there! I think placement of the greenhouse can really make a difference. If you put it to where it will get the first rays of the morning sun, it will have much less time at the coldest temperatures.
I also try to keep it wide open during the day so they get the cool temps. 50s during the day and low 40s at night seems to stop them from pushing new growth. I think this allows them to harden off a bit so when it comes to almost freezing temps, they are already in survival mode. They aren't shocked.