This is a tribe of humans who, through perfect innocence and moral character, have taken to living onto the clouds. The Wind Tribe is actually very similar in appearance to the Gerudo, both having red hair, round ears and clothes cut in the Middle Eastern style, but the Wind Tribe's are more floppy, supposedly to help them move on the winds. The Wind Tribe has more than one male however, and at least some of them, reportedly have red eyes (like the Sheikah). They are the same height and weight as a Hylian, and the men sport beards while the women wear their long hair in buns. They do not seem to wear as much jewelry as the Gerudo do.
Originally, the Wind Tribe lived south of the swamp known as Castor Wilds, where they worked in harmony with the Minish and received advanced gifts from them, including the original armos statues, and the guardian of their ruins Mazaal (with no fear that the Wind Tribe would misuse them, because of their pure hearts and minds).
In fact, given the resemblance between this guardian and the one found in the suspended Tower of the Gods, it seems plausible that it was really the Wind Tribe (and possibly the Minish who may have been represented by the statues that turn into the three Goddesses after Link places the pearls in their hands) who built it. The Tower even had the architectural style typical of Wind Tribe constructions.
Before leaving for the skies, the Wind Tribe was very close to the Royal Family of Hyrule, who were very grieved to see them depart. Apparently they even contributed to building a large shrine to house the remains and the spirit of one of Hyrule's Kings from long ago.
When the wind tribe left Hyrule behind to live on the clouds, they also left behind the Minish. In fact, centuries later, members of the Wind Tribe would even attended to the Picori festival to confirm that the Minish are more than a fairytale. However at least one member of the Wind Tribe had settled in Hyrule Castle Town at the time when Vaati stole the Minish Cap.
At that time, the Wind Tribe was not very numerous. The whole group appeared like a large family, looking after each other. It could be, however, that they were dying off. The tribe lived in a modestly furnished, large building resting on a cloud, which connected to the Palace of the Winds even higher in the clouds. The Palace would later on become Vaati's stronghold and no trace of the Wind Tribe would be found in the nearby area of sky.
Apparently members of the Wind Tribe also had a great gift for finding (and discovering uses for) kinstone pieces and for raising many species of birds, including magical ones such as Zeffa, a very strong, blue quail-like bird that can fly people from wind crest to wind crest. This inclination to raising and training birds, could indicate a connection between the Wind Tribe and the other people dwelling in the sky, the Oocca in addition to both of them having access to technology far ahead of anything the ground dwellers have.
Both the gate in Castor Wilds and a system of fans that control the winds block the path to their homes in Hyrule and on the clouds respectively and are operated through kinstone pieces locks. Their political system is easy to explain. Just like a good family, the younger members look up to the older members, at the time of Vaati's first appearance, an elderly woman. On another note, as thanks for saving him from a ghost haunting him, an old man of the Wind Tribe made for Link the Light Arrows (which, Zelda implied in another occasion, were used by others before the Hero of Time).