As little and big says, if you're on the Brooks, it would take a deluge to get it wet. The underside ( esp. w/o mudguards) is more prone, but a good proofiding befoe will protect it. (Apply that after a ride, it really helps that the saddle is thoroughly warm to get the stuff to go in).
I use the cover if it's really chucking it down, and then the compulsory carrier bag when I leave it. The cover isn't lovely to ride on.