Question: My daily routine consists of washing my hands in the morning, praying Shacharit, and then washing my face on my way out of the house. Is my routine correct?
Answer: The Gemara (Shabbat 50b) states: “One must wash one’s face, hands, and feet every day in honor of one’s Maker, as the verse states, “Whatever Hashem has done is for His sake.” The Rambam (Chapter 4 of Hilchot Tefillah) writes that before praying Shacharit, one must wash his face, hands, and feet, in honor of Hashem.
Nevertheless, other Rishonim disagree with the Rambam’s opinion and write that there is no special obligation to do so specifically before praying (see Meiri’s Bet Ha’Bechira on the above Gemara and the notation of the Ra’avad on the aforementioned Rambam). Thus, regarding our question about whether or not one must wash his face specifically before praying, according to the Rambam, indeed, one must wash one’s face before praying while according to the other Rishonim, one need not do so.
Maran Ha’Bet Yosef (Chapter 92) writes that the prevalent does not follow the Rambam who writes that one must “wash his feet.” He writes that that based on the custom of the world, we certainly do not follow the Rambam’s opinion regarding this matter. Other great Poskim rule likewise (see Halacha Berura, Chapter 4). Nevertheless, this only applies to washing one’s feet and only with regards to this is the custom not to wash one’s feet before Shacharit, especially in our countries where people usually walk around with their feet covered. However, it seems that one should take care to wash his face before the Shacharit prayer; it is indeed proper to do so according the opinion of the great Mekubalim.
This is especially true nowadays when we are much more hygienically conscious than previous generations; it is therefore correct for one to wash his face and wash his mouth or brush his teeth before praying in order for one not to appear repulsive while praying and not to remain with something which disturbs one’s concentration during prayer. Indeed, Maran Ha’Shulchan Aruch (Chapter 92, Section 3) writes: “One must remove anything which disturbs him before praying.”
Summary: One should preferably take care to wash one’s face and mouth before praying Shacharit and not pray first and only then wash one’s face (excluding fast days, especially Yom Kippur). If one has already prayed without having washed his face and the like, one has surely fulfilled his obligation to pray.