A good mud hut sheds water pretty well, and the material for roofing is abundant on savannah that grows tall elephant grass. What you do is leave about a foot between the top of the wall and the roof along both sides to allow for circulation of air, much as we used to do with tall windows that opened at the top here in the US before A/C.

Sweeping the area several times a day keeps the outside free of sheep, goat and chicken droppings too.

[Linked Image from live.staticflickr.com]

"...if the gentlemen of Virginia shall send us a dozen of their sons, we would take great care in their education, instruct them in all we know, and make men of them." Canasatego 1744