One of the biggest challenges with self-driving cars in snow is the snow in the environment -- for example, how do you see the lane markers so that you stay in your lane?
I did the self driving car class on Udacity and it was super effective as a primer for how these systems work in general and framework for solving these problems.
The thing is that it is vastly different from any other scenario a self-driving car will ever experience or train for. Humans on the other hand grow up with snow and know how it behaves, how it covers the environment and what features are prevalent despite of it (and consequently, people not used to snow that suddenly finds themselves in a snow-covered landscape often fail miserably).
Falling snow can significantly cover both video and disrupt LIDAR immensely. Just as our vision, thing is we already know how to cope with it, it is a greatly different problem than driving in good/ok conditions.
In general, however, I agree that doing what a prudent driver would do in the situation is probably not an insurmountable problem.
As a human in a snowy region, who has been in some pretty dicey conditions, I measure the slope of the road. Roads are typically shaped like a triangle, so if your car changes it’s rotation on the axis that is your direction of travel, you know you are outside of your lane. Even my smartphone has sensors for that kind of measurement.