Tengu 天狗 (heaven + dog) are well known among the youkai, monster-spirits. Tengu are spirits of mountains and forests. It used to be considered as a monster-like bird, and the long nose could be a symbol of the bird beak. Some Buddhist texts mention that it derives from a Hindu eagle deity called Garuda.
I read and watched a folktale called こぶとりじいさん kobu-tori jiisan, "The old man with the lump removed." A group of tengu appear in the story, coming from the sky on a cloud and spending the night in a mountain temple.