There are many Japanese legendary creatures and Tengu is one of them. Tengu wears Japanese mountain ascetic hermit's clothes and have wings. Then, their faces are red and have long noses. Their footwears are geta; Japanese wooden flip-flops with a single wooden high rise block beneath the sole.
Literally Tengu means Heaven's dog but it is believed that Tengu brings disasters. On the other hand, some shrine worships Tengu as one of the gods. Therefore you can see Tengu statues at numerous shrines around Japan. Especially Takaosan-Yakuoin shrine located on the Mt.Takao is worshipper of Tengu. Mt.Takao is a extremely popular hiking destination in Tokyo metropolitan area.
Also there is a rumor that European Caucasian whom was seen by local Japanese peasant in middle age made up the current appearance of Tengu. Caucasian has longer nose and the skin color is more reddish than Japanese. Then, probably worn unfamiliar clothes and footwears for Japanese whom had no idea how European looked like in the middle age.