Cars will use LIDAR, ultrasonic, and video for first party sensing.
But a lot of sensing will come from their party. Other cars reporting their position on the road. Their intent and upcoming moves.Details about the environment that they sense. Additional the infrastructure can provide info. The roads can report if cars are present. If there is ice, etc.
Anyways, the issue isn't if there is ice or snow on it's sensors. That will be easy to mitigate. The problem is the ice and snow in the environment that it needs to see through.
How much time have you spent scraping ice off of a windshield where it's gone from above freezing and raining when you parked your car to well below freezing overnight and sometimes even well below 0 F? How many times have you had to dig a car out of a snowbank? If you've had to do it over the course of a few winters you'll know that it's often not so easily mitigated.
I think people either don't know or often forget what a hostile environment winter can be in the the Northern part of our country. How densely packed are the sensors going to be in the road to tell reliably where there is ice, whether the ice is smooth or rough, whether there is snow and how deep it is and whether it is packed or fresh? How long are these sensors going to last when the roads I drive on end up filled with potholes each spring?
I'm sure it would all work great in a laboratory setting when every other car, plus all the roads and traffic control devices can talk. I'm not so convinced that it will work when things are in some state of disrepair as they often are in the real world.