[chryuop]

In my opinion that phrase is wrong (but I am just a student as well, so I might be wrong). It seems that wherever you read it, it was printed on the contrary. In that phrase から is referring to the subordinate clause "I am sad" so the reason becomes "I am sad". Moreover, as far as I know, unless the subject is the same you will not have the topic marker は in the subordinate clause, but in the main claus. Thus at most the phrase in my opinion should have been 私が悲しいですから雨は降っています...which if you ask me sounds pretty weird and unnutural.
I guess the phrase originally was 雨が降っていますから私は悲しいです。

Just my opinion tho...