What if the snow falls. I mean, surely that's not stable.

Well, it can slide, but the snow is hard packed and melts slowly in the spring. I have only driven over the mountain once at Easter time when the snow edge was almost as high as in the picture. And at the top there were skiers. (was in 1977)
I was young and with the courage of youth... we drive the Volkswagen Bubble.
Today, the road network is large tunnels going through the mountain.
Safer for traffic and people. (The part of the road that is outside the tunnels notices when it is snowing and blowing strongly. Then large special vehicles pick up a certain number of cars at the back of the convoy down to better access and visibility.