One fact that is more widely known explains why Urokodaki has chosen to hide his face in the series. If one watches Season 1, Episode 3, until the very end, one will be told by Tanjiro a Taisho secret which describes the reason why Urokodaki began wearing a mask: "I heard that's because demons used to make fun of his face for looking too kind." This is an interesting tidbit especially when we draw parallels between Tanjiro and his Master: not only are they endowed with a superhuman sense of smell, but they are both possessors of an incredibly kind heart which often shows on their soft features — not that we ever get to see Urokodaki's, to confirm this.
What most fans may not know, however, is the real reason why mangaka Koyoharu Gotouge decided to perpetually draw Urokodaki with a Tengu mask. Having roots in both Buddhism and Shintoism, "Tengu are fearsome demi-gods that would protect mountainous areas" (per Eiyo Kimono). Indeed, despite not being a god but a mortal human, the retired Water Hashira also resides in a mountain region and no doubt uses his skills to defend it even now.