Well, I’ll make some educated guesses:
(1) snow accumulates gradually one flake at a time, each gently settling atop the accumulation without mechanically disturbing the pile below too much
(2) snow is usually somewhat sticky, each flake adhering to its neighbors to varying degrees
(3) the rate of snowfall (flakes per square cm. per sec.) is fairly constant over the small extent of the railing (a few feet?).
*(4)*Any change in snowfall rate over time will equally affect the entire extent of the railing.
(5) the railing is straight, smooth, and all one width— another set of constants over the extent of the railing.
(6) wind is probably an important factor, different each time it snows. Wind might not be constant across the whole railing if parts of it are more sheltered than others, i.e., broken symmetry.
So snow piling on railings might have a steep angle of repose which forms a constant cross-section along the length of the railing. The cross-section might be triangular, semi-circular, inverted catenary? or some other geometrically interesting curve, with non-linear features creating, perhaps, aperiodic blobs or defects in spots where wind is gusting. Nature is a great artist…
@philosopher Is your railing round or square?