Is there a Halachic issue with face painting Yiddishe themed pictures on a child’s face?

There is no Issur to write or paint on oneself with temporary paint, as long as one does not also scratch/carve into oneself at the same time.

It is however forbidden for girls to walk around like that in public due to Tznius.

A Moisad should also take into consideration whether the activity is appropriate from a Chinuch point of view.