Would it be correct to use “它” in a sentence like this "它在外面下雪了."？ Just as the title says, would it be correct to use “它” in a sentence like this "它在外面下雪了." or I could just say "在外面下雪了"？
It's not correct. 
The correct sentence is


  外面（在）下雪


In Chinese, as in some other European languages, weather verbs have zero valency, which means that they take no arguments, neither object nor subject. Therefore you must omit 它.