I would suggest that LL is vertical... and so is DL and I don't consider it as horizontal for reactions... there is a horizontal component that varies with the support condition... if you prop a pencil (stick?) horizontally on two fingers of opposite hands and raise the one hand, the pencil (stick) will want to slide off... it has a horizontal component.
Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?
The applied load is a gravity load, so it is always vertical. Reactions are also vertical. There is no horizontal reaction unless there are horizontal forces applied, such as wind, earthquake or people horsing around on the stair and creating horizontal forces.
If a vertical load is supported on a sloping surface, it will slide if the coefficient of friction is exceeded, so the stair must present a horizontal surface to the reaction points.
Technically yes. However, if you also consider the component of the LL parallel to the stair, its horizontal reaction will perfectly offset that of the component of LL perpendicular to the stair. Hence the other guys' responses.
Unless you're not allowing it to move horizontally at both ends then you'll get some horizontal forces from a vertical applied loading. I only mention it because sometimes stairs are 'built in' to rigid elements each end.
That's not the same and certainly not what I was getting at.
I've never seen a practical stair leaned up against a vertical face to generate a horizontal load as a structural system. They are typically supported vertically by discrete supports, with no horizontal reactions unless you are preventing lateral movement to some degree at both end supports. Even if frictionless at the vertical supports for a stair there is no horizontal load required to achieve equilibrium.
