I think it's because defining the angle a ray makes with a line (the normal) is easier than defining the angle it makes with a plane (the tangent plane, to a surface that may be curved).
I think we measure the angle with respect to the normal because by doing so we can explain many phenomenon that happens in the nature due to reflection and refraction of light.May be by measuring the angle horizontally we won't be able to explain those phenomenon so neatly. Or may be we'll be but only in the case of flat objects.
And in the case of reflection and refraction on spherical surface where surface is not horizontal we won't be able to explain all the things without having lots of assumptions.
So for keeping the things easy and clear we measure the angle w.r.t to normal.