춥다 and 차갑다 both mean cold, but 춥다 is generally used with weather or ambient temperature, whereas 차갑다 is usually used with objects that are ‘cold, chilly, freezing to touch’.
Examples with usage of 춥다 and 차갑다:
오늘 날씨가 추워요. The weather is cold today.
음식이 차가워요. The food is cold.
방이 너무 추워요. The room is very cold.
바닷물은 매우 차가워요. The sea water is freezy.
네 손이 왜 이렇게 차가워? Why are your hands so cold?
Also Check : Difference Between 덥다 and 뜨겁다
