I see snakeskins as a way to keep all the strings and hardware from getting tangled up and may a quick system of deployment and stowing. I use what is called a Black Baldrick Bag (after a Blackadder sketch --- see www.dreamshares.com/quotations/blackadder2.html) or a Bishop sack. It is simply a stuff sack with a hole in the closed end for my whoopie sling suspension to fit through. If you sew, a buttonhole will do the trick. The bag is left on when the hammock is being used. When ready to stow, the hammock is stuffed in the bag and closed, then the suspension is unclipped (a carabiner) and then I wrap the sling around the bag and clip it back on itself. You can see the deploying is just the reverse. In my case, I found a large mesh bag and simply clipped between a couple holes for the suspension opening. It allows things to dry a little too.
As with ground camping, you want to put your tarp up first to stay dry. It could be stowed in the open end of the Black Baldrick Bag, which you can't do with a snake skin and a large tarp. Some of the minimalist Hennessy tarps would fit.
Something I have wanted to develop is a storage bag that becomes a weather cover for the head end of the hammock, or perhaps two so both ends could be covered. It would be like a big funnel and held up by the ridgeline. It could be secured with a light line to the other end. The depth would be up to the maker.
Clark hammocks have fabric panels incorporated in each end with the bug screen. It would be possible to make two funnels with a bug screen between and a zipper going all the way around on the head end. The whole works could be stashed in the head end. If you pack is big enough, it could stow your top and bottom quilts too.