Since the mountain forms a spiral, we could do that same curly design for the rest of the movie. The mountain man can have a curly beard filled with snow and icicles:
Our sheep could be big and fluffy, with curly hair. Just need to have some icicles hanging from the end of the fur:
Sheep covered in snow look funny. It would be amusing to see the father ram/sheep come up to the mountain man with a face covered in snow, chewing on a dead piece of grass. Or when the ram gets thrown through the snow, it gets covered:
Or some curly trees
I like the sense of height in this image. We could design our mountain so it looks similarly gargantuan. I really like the ice clinging to the sides of the cliff:
From a technical stand point, I would recommend we have powdery snow. That way, we can use SPH fluids to simulate most of the snow's dynamics.