If its the height of the horse you're measuring then, vertically, from the floor to the horse's withers. Horses are measured in hands.
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If one of the two variables is independent (or explanatory) then it goes on the horizontal axis. Otherwise you do whatever you like.
Roof pitch is measured in "rise over run". In other words, how many inches does the roof rise vertically in 12" of horizontal run. If a roof rises 4" in 12" of run, you have a 4/12 roof pitch.
vertical
I always remember that we pray vertically, meaning vertical is up and down. Works for me.
independent variable