As the kanji letter "布 (nuno)" (cloth) refers, hoi was originally plain clothes of hemp, but nobles chose these clothes for hunting with a falcon because these were suitable for such activity.
布と言う字からも解るとおりもともと麻布製の素朴なものであったが、動きやすさを好まれて貴族が鷹狩りなどの衣装として採用した。