I think a self driving car will do a much better job operating in the rain than a human being. Rain makes it difficult to see and wipers are sometimes worn out and make visibility even worse.
Slick driving conditions are also dangerous for human drivers but these days there are electronic stability systems in place to make it less dangerous to drive in the rain. If you have a car that can turn all traction controls off you can easily see the difference of assisted and non assisted driving in the rain.
I think the bigger problem will be heavy snow. What happens when you park your car at the mall and come back to find the sensors covered in 4 inches of snow? Very curious to see how they deal with that issue.