Interesting concept here. I would find some drivers that will be impervious to water and high heat that can also do so in a down firing configuration. Not an easy set of objectives to achieve.
The Dayton DVC, if I am thinking of the correct drivers, use a coated paper/pulp cone. This is not a good choice in an outdoor subwoofer in my opinion.
I would look for a poly cone/rubber surround or anodized & coated aluminum cone/rubber surround woofer.
Depending upon placement, you will get little to no reinforcement (transfer function gain) outdoors so sealed may not be the best choice here. The sub's anechoic f6 - f10 is about all you are going to perceive depending upon output level.
Enclosure material will need to be well thought out here too. I would recommend a 13 ply, void free, marine grade, Baltic Birch. This stuff is NOT cheap. I would also use PL premium as your adhesive here for bonding your panels. This will hold up better under harsh conditions long term. I also recommend sealing the wood inside & outside the enclosure to prevent swelling of any sort.