why reinvent the wheel?
there are a variety of portable outside shower set ups already available.....cabella's, dicks sporting goods, pro bass shop and others sell them, so do an online search or visit one of these vendors. the ones i've used have walls, roof, floor, shelves for soap, hangers for towels and floors that drain. i've also made a portable one from pvc pipes, blue tarps, zip ties and duct tape....but the ready made ones aren't that costly.
yes you want to set it up where the nature of the ground spot is considered....what will it be like wet?
also if you are wheeling into/out of the spot you might consider a cedar grid/latice portable floor to improve drainage and avoid sinking.
running the cold water lines outside isn't hard (the new ones already have a outside faucet) but hots another issue....so i would use the solar bags that the same merchants mentioned about stock. we use these every year on ragbrai and they make for a very warm outdoor shower. if it's not sunny enough the bags can be filled inside and taken out to the shower....
we want to see pictures of whatever you come up with!!