I know that at one point everyone changed clothes (Noctis lost his collar, Gladiolus - his shirt, etc.). This is because, from what I read, Nomura hired some super cool fashion designer to design clothes for the cast. So I guess it's kind of a fashion statement/motif.

EDIT: Just noticed Cor's wearing galoshes. Ouch. :/ And here I thought we put such trout behind us.