Translation:It is cold outside.
According to naver translate, that should be right, but this may be an issue of "outside" being both a noun and a preposition in English and only a preposition in Korean. For example, "Beside is cold" or "Over is cold" would not make sense. The omitted subject - in this sentence: "It (probably the weather)" - allows the sentence to work. I'm not sure of this, but it seems like a logical explanation. Can anyone confirm my suspicion here?
It is different because "it is cold outside" is more natural in English, but there is nothing technically wrong with "outside is cold" and I think the latter is a more direct way to think about the korean sentence in english. I also prefer that answer to "it is cold outside" because that formation comes from rules that do not apply in korean.
에 is a location marking particle and indicates where or to where the subject is or will be. 에서 indicates an action being done at a certain place by the subject, or from where a directional action is taking place.
I've used 밖에 춰워(요) with Koreans before and I've heard them use it too, so I know it's allowed. Whether or not it's technically grammatically correct though. I'm not really sure lol
Hope that helps!