Hmm. What region of the country was this in?
The mud would wash right off in wetter climates. But the carpet + plastic sheeting would no doubt keep the weather out for quite a while in many U.S climates. You could also invest in half a dozen cans of silicon waterproofing spray (like CampDry), and spray the carpet. I think it would repel water better than most tents or teepees. I have a few carpet scraps outside, where I was working on a project and didn't get around to picking up all the scraps. They get rained on all** the time, and a couple of times I've picked them up, out of curiosity, and been shocked to find that they seemingly hadn't held on to the water. They also haven't molded or mildewed. I have no idea why. The scraps are of newer, modern carpet . No idea what they were treated with.