We already let computers control cars because they're better than humans at it when the weather is inclement. It's called ABS.
There is an inherent danger to driving in snow and ice. It is a PR nightmare waiting to happen because there is no way around accidents if the cars are on the road all the time in rust belt snow.
There's always an inherent risk to driving, even in sunny Phoenix, Az. Winter dangers like black ice further multiply that risk but humans still manage to drive in winter. Taking a picture/video of a snowed over road and judging the width and inventing lanes based on the width taking into account snowbanks doesn't take an ML algorithm. Lidar can see black ice while human eyes can not, giving cars equipped with lidar (wether driven by a human or a computer) an advantage over those without it, and Waymo cars currently have lidar.
I'm sure there are new challenges for Waymo to solve before deploying the service in Buffalo, but it's not this unforeseen gotcha parent comment implies.
As far as the possible PR nightmare, you'd never do self driving cars in the first place if you let that fear control you because, you you pointed out, driving on the roads is inherently dangerous with too many unforeseen complications.