How hard would it be to keep part of my zone 8b vegetable garden above freezing? I'm thinking about protecting the part that contains tomatoes, okra, tomatillos, and basil. How expensive would that have to be? Would you recommend doing it?

You could try grow tunnels.

I second what Daisy said. Tunnels are probably your best bet, but I'm not sure about those particular vegetables you want to keep during the winter. You might be better off with cool season vegetables for more success. A good resource for you would be to talk with someone at your local university extension.

My daughter is a great believer in grow tunnels and manages to keep tomatoes alive for a good portion of the winter. I think she lost them in January when the outside temps hit some minus number. BUT, after awhile, the tomatoes start going weird and mealy so she usually pulls them earlier. She also says its not lack of heat that stops her veggies from growing but lack of sun because we are so far north. You wouldn't have that problem. Her carrots, onions, kale and beets do fine though. She also moves her pots of Sunchokes into them. Minus numbers won't happen in zone 8.

When I lived in zone 8, I grew peppers against a wall without cover - just the protection of the wall. They lasted for 7 or 8 years before an especially cold year did them in.

I'm not trying to harvest them in the winter, just to keep them alive so they'll be ready sooner next year. It seems a shame to plant these tender perennials and grow them nice and big, then have to start over with babies the next year.