Imo, the best material I have found for projects like that is closed cell pvc. it's used for a lot of home siding and trim applications, but works out well for any exterior projects.
There's a number of brands out there,
Azek -
http://www.azek.com/products.php
Versatex -
http://www.versatex.com/product_offering.html
Certainteed and many others.
Some sell full size sheets, 4' x 8', (and larger) and some sell only trim boards. I'm not exactly sure how big their trim boards are, but I think they have up to at least 12 inch's wide, usually up to one inch thick, (maybe more) and that should be ok for making a cabin, (bi-fold) door. I think it will be easier to find the trim boards, and cheaper too.
Not sure if places like Home depot or Lowes carries these specific brands, but they should have something similar. Might want to check their websites for dealers. I believe 84 Lumber is a dealer for either Azek or Versatex. You can check out any local lumber yard too.
I used Azek for a small project and it worked great. It's lighter and easier to work with than polyethylene, (Starboard). Cuts, drill and screws together easily. You can also glue it together. It's paintable, but not necessary. Again, imo... this stuff is excellent for doors, cabinettes, drawers, trim etc.