I think I have idea of why Mickey and Riku where the trench coats. They are trying to hide their identity. The organization wanted to kill Riku so he doesn't know who might be after him, so he needs to hide. In current descriptions of the story line it said something about Mickey's past being part of the story. Maybe Mickey is also hiding himself. Since the unknowns are have the huge hoods, what better way to hide their faces than with on of those coats.