Re: A traditional gift is a clay horse, which they paint in bright colours.
You have asked several very similar questions recently. It is not just a question of labelling a clause with 'who/which' separated from the main clause by a comma 'non-restrictive and one with 'that' and no comma 'restrictive'.
A non-restrictive (non-defining) relative clause simply provides more information about something that is defined in some other way. Your first sentence is a about a clay horse. The fact that it is painted in bright colours is extra information. The second is about not just any sort of clay horse, but about a brightly painted clay horse.
Context is always important; labelling is rarely important.