1. What does it mean?
얼죽코 abbreviates 얼어 죽어도 코트, literally 'a coat even if I freeze to death.' It jokingly describes a strong preference for a styled coat over a bulkier winter jacket, even on a very cold day.
Also written or said as eoljukko
2. The nuance
The wording is comic exaggeration, not an instruction to ignore cold or discomfort. Someone can call themselves 얼죽코 and still choose warmer clothing when needed.
3. Examples
“얼죽코라더니 오늘은 패딩 입고 왔네.”
You call yourself a coat-at-any-cost person, but you came in a padded jacket today.
“코트가 좋지만 한파에는 얼죽코 고집을 쉬기로 했어.”
I like coats, but I decided to put my coat-at-any-cost habit aside during the cold snap.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.