tried the milk cleanser this morning. no salt. just cotton wool soaked in milk and rubbed onto face then risned off with water. surprised that it actually removed dirt from the face.
I suppose the salt is in there as an exfoliant; bit sharp, though, I'd have thought...?
The oils and fats in the milk would lift the dirt.
Our skin produces a very fine oil, and any dirt gets caught in that oil. Soap works by adhering to the oil and lifting it off when rinsed away. Any oil works in much the same way: it would mix with the oil on the skin, and then when you wipe it off, both oils would come together, together with the dirt.
The oil on our skin is fine and light enough to wash off in sufficient water: think how we can get squeaky clean after swimming.
Someone once told me that some Gypsy tribes would cover themselves in turmeric, and it would stain their skin a kind of golden colour. No idea if this is true or not: if so I guess they must have left it on for some time and repeated it fairly often. I suppose, as travellers being exposed to new bacteria and pathogens as they went along their way, covering the skin with something with so many medicinal benefits was a good prophylactic. If true, I'm guessing it was the Romani, who had links with India, where turmeric is a native plant.