I catch a cold. X
I caught a cold. O
caught は過去形
I CAUGHT a cold because I was wearing light clothes even though it WAS cold.
過去形にしましょう。
I was wearing light clothes = 薄着をしていた
I was dressed lightly = 薄着をしていた
I caught a cold because I was dressed lightly even though it was cold.
It was cold outside and I didn't wear enough clothes, so I ended up catching a cold.
この場合、次のような言い方ができますよ。
ーIt was cold outside and I didn't wear enough clothes, so I ended up catching a cold.
「寒いのに薄着をしていたら、風邪をひいてしまった」
didn't wear enough clothes を使って「薄着をした」ことを言うと自然でしょう。
「〜してしまった」は to end up ~ing を使って言えます。
ご参考まで!