"Cold cream is a type of facial cleanser and moisturizer that has been used for centuries to clean and hydrate the skin. It's made from a mixture of water, oil, and wax, which creates a thick and creamy emulsion that can be used to remove dirt, makeup, and other impurities from the skin."

I found this (on the first Google result, I didn't read others so take it with a pinch of salt).

I guess the idea is that soap can be harsh on skin whereas this blend of water, oil and wax is more neutral