In your area, cypress would be the very best choice. I know there once was a factory in NO for these, they were featured on TOH or some similar program. They may still be in business, and it may be worthwhile finding a source as nearby as possible, because shipping on large delicate items is most certainly a $ factor.
Other good woods, considering you have extreme climate issues: south american mahogany (hard wood) spanish cedar (very soft wood) tiger wood (medium-hard, wish I could remember the other name for it) . these are all decent for rot resistance, and are paintable. True heart cypress will last forever. Cypress sapwood is no better than pine, unfortunately.
It's somewhat correct about the B&B construction vs. louvers, but the other issue is that louvered shutters have a mortise and tenon frame, and those joints collect water. If the wood cannot withstand staying wet without beginning to decay, the shutters are doomed. Even B&B shutters would benefit greatly by painting the components separately before assembly so the overlap area is "waterproofed".
Casey

Unless the shutters are under a deep porch where they will get no rain, the pine will not last, and is a waste of money. For $100 per shutter, you are not going to find anything worth buying, especially a louvered shutter; they are labor intensive to make. If you would like to get prices on cedar, look at the ads in the rear of "Old House Journal", Fine Homebuilding" ,etc. . If I was going to pay to have them built locally, I would use only vertical grain, heart cypress (first choice),or clear heart vertical grain redwood or cedar, or genuine Honduran mahogany ( not Philippine mahognany which is just a marketing name for meranti). There are other rot resistant woods, but they do not hold paint well.

thank you very much sombreuil and troubleseekeral. Y'all know your stuff!

Why is it that I tend to like the more expensive and harder to make things? I want inset cabs that are costing me more too! My husband says I should go with the board and batten, but I've got my heart set on the louvered with the little pole in the middle.

bmh4796

Question for everyone:
Would treated pine work?

Pooh Bear

Pressure treated pine would work---but, finding someone willing to subject themselves and their tools to the possible ill effects of milling that wood will be difficult.

Plus, PT pine is often the worst grade and the knots will be a big pain.

If I were wanting no-maintenance exterior trim, I would look at PVC lumber. It comes in many popular sizes---1by4, 1by6, etc.-----has a grain cast in, and can be worked with most woodworking tools. Painted, it will only require occasional touchup and be otherwise carefree.

"Pressure treated pine would work..."

Not really. PT prevents attack of the wood fiber but does absolutely nothing about wood movement from moisture.
Add to that the stuff is very wet and warps like crazy as it dries out again and small sections will turn into pretzels as they dry.

but, finding someone willing to subject themselves and their tools
to the possible ill effects of milling that wood will be difficult.

What ill effects. Especially since CCA was phased out.

I was thinking of maybe this person could get some
6x6 treated timbers and have someone with a bandmill
to resaw them into 1/2 inch stock to use for the louvers.
Only problem I see with this is the grain orientations.
Since timbers usually contain the pith the resawed
lumber would be badly subjective to checking and cupping.

Pooh Bear

I wouldn't buy pine wood shutters as they don't hold up nearly as well as cedar does.

You can find exterior louvered shutters at www.shutterland.net. The make high quality shutters made of solid incense cedar, which is decay resistant, has low shrinkage and is a very straight wood.

Here is a link that might be useful: ShutterLand Exterior Shutters