Sure, eventually it will be better. But I wouldn't be shocked if bad-weather automatic driving lagged at least a decade behind what they can get away with in Arizona. It's a significantly harder problem, and much more difficult to generate reams of data to test against.

Worse, the risk shoots way up, and people will be much less tolerant of risks that aren't under their control. "Driver Ends Up In Ditch" is never news in places with real winter. But "Google Almost Killed My Family" sure will be.

Places that only get a few days of snow are typically paralyzed by that snow (schools close etc), so the autonomous cars being paralyzed aren't really a problem in those areas.

But for a lot of northern and central europe, northern US, canada etc where people are used to changing tyres and driving for several months in snow, the autonomous cars will have a harder time.

On one hand like you say, they can see things we can't. But on the other hand, there are zero lane markers, and sensors are typically covered in snow.

For example: I have parking sensors and a rear camera on my car and those are completely covered a lot of the time in winter. I still use my car and just ignore that the parking sensors scream constantly and the rear camera shows the inside of a wad of snow. That situation would be worse for an autonomous car because those sensors aren't just nice-to-have, they are fundamental to to the operation of the car.