Larry, The map is actually the official USDA map. If you go to this post: What is My Garden Zone. there is a link about halfway down the page that will take you directly to their site and you can put in your zip code and it will give your exact zone. You are going to be Zone 9 or 10 so a greenhouse is probably overkill for you.

Our early plantings of potatoes go in around mid March. But they have to go in a cold frame so that I have a way of protecting them from frost which we have until mid May, sometimes early June.

I’ve planted as late as November before too, but that late in the year I risk the ground being frozen so I usually get it done in Mid October.

One of the fun projects I could never dream of doing here in cold Utah!!

Here in hot, dry AZ in Zone 8/9 I’ve found I can overwinter potatoes if I put milk jug solar heaters (jugs filled with water) in my hoop houses. The main thing I have to watch out for is to not overwater the raised bed their planted in. As with cooler weather zones the spuds will rot if they are too wet. I usually put my main crop of potatoes in during the first week of March–depends on how cold it’s getting at night.