Experience With Desert Cultures
I spent some time in the middle east, and I observed a few things. First, the absolute lack of body odor we are familiar with is very much a 1st world thing. People in Afghanistan or Iraq STANK. But after a while you come to realize, that's just what people naturally smell like. Our absolute odor neutrality is created by our deodorants, antiperspirants, perfumes, colognes, shampoos, and body washes which we apply religiously utilizing water piped in from dozens, or even hundreds of miles away. After a month in the sandbox you quit noticing that everybody smells like feet and armpits, and upon returning to your comfy 1st world country with lots of water realize from the annoyed looks on everybody faces that you don't smell good. In the desert, body odor is something you get used to, and eventually stop noticing.
Something I saw a lot of was sand bathing. Afghans, especially the tribal, would use handfuls of sand as an abrasive to rub off filth. Another thing was, what you or I would consider stagnant and fetid water is a bath to them. Water is a scarce commodity in the desert, so if you find some you can't drink that means its bath time. I watched people, often times my native friends and acquaintances stripped naked squatting in puddles of brown, dirty water vigorously rubbing handfuls of wet sand under their armpits, their feet, and other... ahem... smelly areas. Initially my holier than thou 1st world sensibilities were offended, but then I realized it makes perfect sense. They haven't had a wet bath in a month or two, here is some water, and its not good for drinking so hey, why not have a bath?
Finally comes how you wipe your butt. Well, there's no toilet paper. There's no leaves. So what now? Well... At least in the middle east, the go to solution was your hand. Now, this sounds gross, but if you do some walking in their shoes it makes sense. You use your non-dominant hand, then you use fistfuls of sand to dry and abrade it off. In Islamic culture the left hand is seen as filthy, and no matter how clean you never EVER point, gesture, grab, shake hands or do otherwise with it. At least in the desert culture I was interacting with, that was your doo-doo hand, and you never did anything with it unless you wanted to absolutely flip the rudest of birds at somebody. Even just gesturing with it to somebody innocently was literally saying "You are feces. I use my feces hand to deal with you, because you are feces." I once accidentally offered my interpreter and long time companion a cigarette innocently and ignorantly using my left hand. The look of hurt and anger on his face was soul destroying. I apologized, crushed it under my boot, then offered him one with my correct hand. Who would think a lack of easily accessible water could have such subtle nuances on a people as to influence their body language in such a strong way?
Bottom line being, not having an abundance of water changes the game a lot, and can have some pretty far reaching cultural effects. I hope sharing a few I noticed can help you in some way.