While I've seen both men and women building Hadza huts, much more often it is women (pictured). The sexual division of labour lit has zeroed in on hunting-vs-gathering; but much less is said about women's differential contributions to water-fetching, food-preparation, cooking, and house-building.
Duncan Stibbard Hawkes
The sexual division of labour regarding house construction shows a very consistent pattern cross-culturally: women usually construct the shelters in nomadic societies, while in sedentary societies men do it.