We've seen a lot of pictures of people in a muddy clay, almost like a pottery clay, does anyone know where to get it from?

Try googling "artists supplies" or similar. Pottery clay can be purchased in relatively small qualtities and mixed with water to produce different thicknesses. It's handled when making things on potters wheels, and used in school art classes, so you won't come to much harm, unless you start eating it.

Messy supplies does some clay, not sure if it's the stuff you are looking for.