Waymo definitely operates on bad weather. In fact, that is when I use it most since I don't want to walk or bike in the city when its pouring. The wait times are longer on those days.
City driving is very chaotic. Though speeds tend to be lower so likely accidents would be just fender benders. They don't operate on freeways.
As I understand it, they limit their range to a few cities in the American Southwest and West Coast, and don't operate in bad weather.