衣替え and 着替え: Seasonal wardrobe changes and a change of clothes
Compare seasonal wardrobe changes with changing clothes or a set of clothes to change into. In 着替えを一組, 一組 counts the clothes brought, rather than a completed act of changing.
衣替え as a seasonal wardrobe change
衣替え（ころもがえ） means a seasonal wardrobe change. In 「週末に衣替えをして、厚いコートを押し入れにしまった。」, the speaker changed the seasonal wardrobe over the weekend and put a thick coat in the closet. The activity organizes clothing for the season.
In 「学校では六月になると制服の衣替えが行われる。」, the school makes its seasonal uniform change in June. The sentence describes the uniform practice at that school.
着替え as an action or clothes
着替え（きがえ） can mean changing clothes or a change of clothes. In 「運動の後で着替えを済ませました。」, the speaker finished changing after exercise. 済ませました makes 着替え the completed action.
In 「雨に濡れたときのために着替えを一組持ってきました。」, the speaker brought a set of clothes in case they got wet in the rain. 一組 counts the set of clothes brought, rather than the number of times someone changed.
A seasonal change, an action, and a set of clothes
衣替え focuses on a seasonal change of clothing. 着替え focuses on changing what someone is wearing or on the clothes to change into. Putting away a thick coat and finishing a change after exercise describe different scopes of activity.
In 着替えを一組, the counter 一組 and the verb 持ってきました make the clothes themselves the object. 雨に濡れたときのために gives a precautionary purpose; it does not report that the speaker already got wet or changed clothes.
Does 一組 in 着替えを一組持ってきました mean that one act of changing clothes was completed?
Show the answer and why
一組 counts a set of clothes brought to change into. 着替え refers to the clothes here, so the sentence does not describe a completed act of changing.