For substantially less crazy conditions, you can infer where the lanes would be by (a) looking at the spots of the road you can see, (b) prior knowledge of the road from experience, and (c) looking at oncoming cars and the flow of traffic, and driving in a way that doesn't surprise them. Though it's likely the case that you shouldn't be driving in these conditions anyway.
You mean carefully get to the nearest settlement as soon as possible? Some of these storms can last for days at a time. Stopping to wait it out in the middle of nowhere, especially if you don't have a full tank of fuel to keep the car warm for extended periods, is a pretty scary situation.
While I think it's plausible to teach a self-driving car to drive in snow (like I do, generally following in the tracks of the cars ahead of me), I honestly think this is one of the best justifications that cars should continue to have steering wheels and pedals: Because automated snow driving is going to take a lot longer to become a solved problem than fair weather driving.
But I wonder about the snow though. How does the car know where to go when there are no identifying lane features? Maybe its not as hard of a problem as I believe it to be?