It is forbidden to wear make up on Shabbat on the basis of two prohibitions: One is on a ‘smearing’ such as smearing lipstick, which is a direct Torah prohibition. The other prohibition is ‘coloring’ and is forbidden by rabbinical ordinance.
Regarding the application of facial powder, there’s a difference of opinion among adjudicators. According to Rav Ovadiah Yosef zt”l, its application is permissible, since it does not involve coloring and provided that it is not mixed with a paste that sticks to the surface of the skin so as it does not fall under the category of ‘smearing’.
But Rabbi Shlomo Zalman Auerbach zt”l and Rabbi Moshe Feinstein zt”l disagree and rule that this would be forbidden based on the prohibition of ‘coloring’.
Though it is important to note that it is difficult to know which powders contain cream or paste and which do not. Therefore, the correct approach would be to refrain from using them on Shabbat altogether.
