I suspect it will know where the lane markings are better than human drivers. They are mapped ahead of time and the car can likely localize itself via other landmarks to determine where they are without being able to see them.
The harder part is driving like a human and detecting that a path has been made in the middle of two lanes in heavy snow and not obeying the lines at all.
The first idea seems like it would require a lot a lot of data stored in the car. Is it feasible? And even so, to be that dependent on matching up with existing pre-mapped data suggests a system that would be quite slow to roll out across a country.
Easy, my dumb level-0 car can tell me when it's icy. And finding lane markers is one of the easiest tasks in self driving (the hard part is knowing when to ignore them).
You're being downvoted for the flippant and dismissive tone of your comment, but I do wonder how computer-driven cars will determine when it is acceptable to violate lane markings and road signs. Boston in winter is more than just traction control. There are snow piles that might be icy, ridges left from a plow, shifting conditions, and bad visibility. I suspect it IS a hard problem.
Lane markings are a fraction of the triangulation.
We ourselves identify and confirm other urban waymarks via captcha which feeds the nav data -- bridges, signs, hills, hydrants, chimneys, lights. There is mass live verification from android auto in vehicles. There are many yearly layers of street view images and scans.