The first time this happened to me what I did was get a sheet of heavy cardboard (cut from the side of a large cardboard box), and punched four holes near the middle (but a little closer to one end). Then I passed two lengths of cooking twine through the four holes. Then I cut open a garbage bag and completely covered the "top" side of the cardboard and taped it down on the underside. Now you have the perfect rain cover. Just tie the twine around the handle, and you'll have a light-weight "roof" for your WSM. The fact that the holes were not made right in the middle will mean the roof will flop one way, point this side into the wind, and tie the roof so that the long side is on the opposite side as the vent. That'll prevent rain getting under the roof to the lid, and allows the vent to freely do its business.
I have been meaning to come up with a better solution, but this one has worked so darn well I haven't needed to so far! My bit of cardboard has lasted several boughts of rain, and many more boughts of drizzle. The only thing is the garbage bag, maybe due to the heat of the smoker on the other side of the cardboard, maybe due to age, is slowly starting to shrink. To the point where it is starting to kink my roof. Still works well though!
If the description above isn't too clear to anyone, let me know and I'll take a photo.