Q. Is one allowed to use blush powder or even other non-colored powder on Shabbos as it is not something that remains permanently on the face?

A. Shulchan Aruch (O.H. 303: 25) rules that a woman should not color her face on Shabbos, as this is included in the prohibited melachah of tzoveah (dyeing). Mishna Berurah (ibid. 79) explains that it is only a rabbinical prohibition as there is no biblical tzoveah on human skin.

However, for even the rabbinical prohibition to apply the coloring agent has to adhere somewhat to the surface. Spilling a tinted liquid that can be easily removed from a table is as tzoveah, as placing a colored tablecloth on it.

Poiskim disagree on using cosmetics. Horav Ovadia Yosef Zt”l writes (Yabia Omer, 6: 37) that there is room for leniency regarding face powder, for the red color that the Talmud (Shabbos 95a) prohibits to apply to one’s face on Shabbat involves actually coloring the face, whereas cosmetic powder does not stick to one’s skin and eventually falls or wears off, as talc powder does and is therefore not considered coloring at all. Similarly Igrois Moishe (O.H. 1: 114) permits when the cosmetic powder does not adhere to the skin.
However, many Poskim rule stringently since in reality, modern cosmetics are designed to remain on the skin and are promoted for their staying ability (39 Melochos 3 p. 742).
Shmiras Shabbos Kehilchosso (14: 59 and note 158) quotes Horav S. Z. Auerbach Zt”l, that if one’s intention is to enhance the shade of the skin even if it is for a short while it could constitute tzoveah.

Horav Shlomo Miller’s Shlit”a opinion is similar.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a