In this case, I think it’s quite literally Normal a.k.a. Gaussian:
Here’s what I think is happening. On windless days with powder, the snow dribbles off the edge of the roof (just above the center of the hump). Flakes drift down in a random walk. The railing terminates the walk after about four feet, by which time the distribution of flake positions has already reached the Normal you’d expect from the Central Limit Theorem.
Enough of the geek stuff; I think I’ll go ski the field.