I'm in Austin, but trust me totally enclosed are A: hard to find, and B: expensive. We opted for covered and it still cost us $130 a month. All the more reason for us to buy some land, but unfortunately that's not cheap around these parts either. But we also don't want to retire here, so we're looking north (far north... Amarillo north).
I think you're going to find that there aren't loads of options for completely enclosed, so you probably are going to have to look at covered.