Translation:The school is cold.
치갑다 means "cold to the touch" while 춥다 means cold when speaking of the weather or the temperature in a room for instanse.
이 의자가 치가요 (this chair is cold [to the touch]) 오늘은 날씨가 추워요! (the weather is cold)
We don't put the object marker 을/를 because the verbs are descriptive (adjectives) and not active (verbs) so they don't need an object. I've used the subject marker 이/가 instead
I wrote "School is cold" and got it wrong. I reported it and I got "You need the article "The" here." Why is this? "School is cold" is a perfectly valid sentence.
"School is cold" implies that in general, schools are cold. It's too general of a sentence, and the subject marker "가" means that it cannot be a general statement. So, "The school is cold" is the only acceptable answer.
춤 does. A common expression is 춤춰요 (to dance). Literally it translates into "to dance a dance"