Note that none of this reflects my opinion, and is purely as objective a summary as I am capable of.
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There are many varieties of things in nature you can use to wipe with, in contrast to the modern choice which has been reduced to white paper with or without printed flowers.
One can carve sticks out of firewood, and use them to scrape residue off. It was important that the sticks had a smooth and sharp edge. They take about a minute to make. They are disposeable, and you could make them ahead of time. When you cut wood with an axe, you get a lot of tiny pieces of wood left which are great for this. You could not use human poop as manure in situations where the used sticks would cause trouble. You did not wash your hands, because you only held onto the end of the stick that hasn't been in your butt.
In case you were out and didn't want to make sticks, you could use moss. Or fruticose lichen (tree moss, old man's beard). The lichen is better than moss because moss is wet. In an emergency, snow works, but it is very cold. Hay and other forms of dead grass work too.
This worked because poop was less sticky in the old days. The types of food they ate made their poop come out in solid pellet form. They did get stomach bugs with the associated loose stool, but simply had to take it for the nuisance it was. Maybe try to get hold on some water to clean off.
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Edit: s/burning wood/firewood/ lest someone gets a really stupid idea...