춥다 is a verb. It is also irregular. 춥 is the verb stem (the 다 means "to".) In writing 밖 춥이에요, you are treating the verb stem as if it were a noun. noun + 에요 (예요) Means it is a ....... So, you must conjugate the verb 춥다. Use this pattern: verb stem + (아, 어, 여) 요. (아 for bright, 어 for dark, and 여 for 하다 verbs) examples: 오다 ---> 와요 (오+아+요) 먹다 ---> 먹어요 (먹 +어+요) 하다 ---> 해요 (하+여+요) Are you still with me? As I said, 춥다 is an irregular verb, so we drop the ㅂ from the stem and then add 어 since the vowel in 춥 (ㅜ) is dark. 추 + 어 +요. = 추워요. Did I lose you? If so, let's try again with regular verbs only until you understand. :) The most important thing is that you understand what this means: (아 for bright, 어 for dark, and 여 for 하다 verbs) As for the question in your title. 춥다 means "to be cold" (verb) 추은 means "cold" (adjective) which is created from the verb.

밖은 춥이에요.(x) 밖은(or 이) 춥습니다.(o) 밖은(or 이) 추워요.(o)