Black coat
This Black Cloak (sometimes called an Organization coat) is a common form of attire for many characters in Kingdom Hearts. It protects the wearer from the darkness in various ways, and in some cases, from detection methods available to the those who wield darkness. It is assumed that this cloak is worn by those who regularly travel through the Corridors of Darkness. It appears that the black cloak is granted to those who travel through the Corridors of Darkness as a symbol of their ability to resist the potential corruption in doing so.
Somehow, when Riku and King Mickey cast their cloaks off, the black gloves, pants, and boots worn under the cloak disappear. Furthermore, any trace of the wearer's clothing under the cloak disappears, such as Riku's collar, jeans, and sneakers in his second attire, or Mickey's trademark white gloves. All these hint that donning the cloak transforms whatever clothing the cloak's bearer is wearing under it into the black gloves, pants, and boots seen on all the cloak's wearers.
It also seems to provide insulation, as Riku (And possibly Xigbar) were able to travel on the mountain in the Land of Dragons, seemingly unfazed by the cold and snow. But Sora, Goofy, Donald, and Mulan were also able to. This can be explained, however. Sora's magical clothes probably blocked the cold. Goofy had fur, and Donald had feathers. Mulan is probably just used to the weather.
Organization XIII
A common misconception about this cloak is that all its wearers are members of Organization XIII. It is true that all Organization XIII members wear these cloaks, though. The form differs for each member; each member wears the main zipper at a different height, and some members' cloaks are thinner in certain areas. For instance, Axel wears his cloak very tight against his arms while Xigbar's zipper is unzipped very high compared to the other members. Additionally, Vexen's cloak extends all the way that it covers his feet like a gown, compared to the rest, as does Demyx, whose shoulder area stands out much more than other members, also. Also, Roxas wears what appear to be black sneakers, while Larxene and Xion wear heeled boots.
Other wearers
The first person to wear this cloak outside of Organization XIII was Riku. He is first seen in this cloak fighting with Roxas in the "Deep Dive" movie. Along with this cloak, Riku wore a blindfold across his eyes. Riku was given his Black Cloak by DiZ so that he would not be tracked down by the Organization XIII.
The King was another person who wore this cloak. He was seen in a version of "Deep Dive" in it, and he was even seen in Sora's Awakening scene with that same cloak, while he was coming to Sora and company's aid. What's interesting about his cloak is that it is much smaller since it's catered to his body. Even the hood is sewn just for Mickey, with places for his ears. When Goofy is injured after the fight with Demyx, he removes and discards his cloak and charges in the Great Maw.
In Kingdom Hearts coded, a new mysterious figure is seen in the black cloak. Due to the so-far enigmatic nature of this being, it is unknown how he acquired it, if outside of Organization XIII affiliation..
