The rain will most likely lower your pH, but its not the end of the world.
In all honesty, the total alkalinity will be more affected than your pH by the rain water. That, in turn will affect your pH, but pH and T.A. fluctuate in hot tubs enough that I can't see you ever even noticing.
Chas had a great point about debris from the roof or trees getting into the tub. Get enough in there, and it could deplete your sanitizer pretty darn fast!
The best thing to sit in weather wise in your hot tub is a heavy snow fall! Everyone should get to experience that as much as possible!