Not being as brave as W_D, I just do sponge baths in my tent, using a rag with my cooking pot. The pot is just outside the door (left open a couple inches) to avoid spills. Not only is this method far less breezy, but I don't have to worry about someone's walking by at the wrong moment. I usually have a cup of lukewarm water left after dinner, and that's sufficient. I do use a wet wipe daily on "strategic" locations, and use hand sanitizer after toileting and before handling food.
I take a 2 gallon ziplock bag as a "washing machine" to rinse out socks and, if necessary, underwear or other clothing. All done a couple hundred feet from water sources, and, of course, no soap. I also use this bag if my hiking clothing is wet at the end of the day--it goes inside the ziplock and in the foot of the sleeping bag. It won't be dry in the morning, but at least it won't be cold!
Like W_D, I pack out all TP, wipes, wrappers, and other garbage!
May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey