Besides looking for a source of the minhag of shat"z to wear a kittel for Tal and Geshem (I couldn't find it, and I have limited internet access where I am, now) what is the reason for it?
I asked my shul's chazzan about this. I received what I, personally, consider a "partial" answer, so I'll relay it, for now, and hope to add more as I discover more.
Geshem is given to us "conditionally" and at the time of Succot, we are "judged" for our worthiness for rain. Judges wear robes, so the kittel is similar to the robe that the judges wear.
The chazzan didn't explain Tal. So, this requires a bit more research.