Sometimes, it's hard to give a hard-and-fast rule, one way or the other. (Remember that the comma is to represent a pause in the spoken words, and the above sentence can be validly spoken with or without the pause, with subtly different meanings.)
Without the pause (or comma) it's merely a weather report. With the pause it's contrasting what's going on elsewhere with the weather outside. It's a matter of emphasis. The pause draws your attention to the word "outside", and whatever that is being contrasted with (presumably some goings-on inside). Either is correct, depending on the intent of the speaker/writer.
(Though neither choice, by itself, would clarify Grouch Marx's statement that "Outside of a dog, a book is man's best friend.")