I agree, this could be a very interesting project. I would think that you would need to do several tests to determine what the fundamental frequency is of the horn, and all of its dominant harmonics. These are what produce the " sound " of the horn. From there you could, as suggested above, design filters to separate these frequencies, and measure their levels. Once the levels are determined, a specification could be set.
The information could be displayed as a set of levels, showing which frequency needs adjusting.
One difficulty could be how each device under test is adjusted to either produce more or less of each required frequency. From what I recall, most car horns only have one adjustment, which basically alters the fundamental frequency, and overall loudness, peaking at its natural resonance. The mechanical properties of the horn itself will determine the harmonics. I would guess that since someone has designed the horns already, the harmonics should be taken care of, it is more a matter of adjusting the fundamental. This could leave the testing to be a go-no-go test, if the horn can be adjusted within the specification, it passes, if not, it is rejected, since I doubt you would want to start altering the mechanical properties of each horn.