Cold paint refers to the finish of a pottery/ceramic item.
A cold painted item is fired in a kiln, typically with a clear glaze. The item is then decoratively painted after the firing. The paint is “cold”, not fired on, and tends to flake easily. Cold paint can also be done on an item that is fired in a kiln, but completely unglazed.
In the example shown, the purple paint is flaking off the jar. And if that jar was washed or cleaned, most likely all the paint would come off.