Snow + stairs + ski boots = potential trouble.
The average annual snowfall in Taos Ski Valley is 305 inches. Uncleared snow quickly becomes a major problem; as shown by the photo from an unoccupied residence. Even when kept cleared, stairs and walkways present slip hazards from snow trapped in the boot treads.
Entrances and stairs should be designed to remove snow and keep it outside the building. Open grating stair tread material accomplishes this quite nicely; just don't go barefoot in the summer!
A single 12" tread works well for a private stair. Public stairs need a shallower rise and a deeper run (say, 5:14 rather than 7:11) to accommodate ski boots.