I've never heard the term "Fold", is that a maybe Southern word for festival? Wow this girl can sing! I wish I could've heard her finger picking style with this. Seems her guitar did not plug into the sound system.
I think "fold" here is used to describe a barn or a pen. Like you would round up the sheep back into the fold. They had to move the shows out to the barn when they had too many visitors, so they just started calling it the Carter Fold. :)