Unsound, many horns do sound quite nasty. I have yet to hear a prosound hornspeaker that doesn't, especially at high volume levels.
Two potential sources of nastiness are frequency response problems and diffraction. Horns all need some sort of equalization, and usually fairly complex equalization, before their frequency response is reasonably smooth. Not all designers go to the trouble to smooth the frequency response - perhaps because many horns still sound edgy even after they measure smooth. Which brings us to the second problem: Diffraction.
Diffraction occurs where there is a fairly sharp discontinuity in the horn flare or profile. For example, many horns have a fairly sharp-edged mouth, which results in diffraction at the mouth. Others deliberately induce diffraction within the horn to widen the radiation pattern. Diffraction has little measurable effect on the steady-state frequency response curve, but it's audible because of where it occurs in the time domain: Just a little bit later than the original sound. The ear is good at masking (ignoring) a lower-level coloration that occurs at the same time as the main signal, but very poor at masking a coloration that occurs later in time. Also, the ear's sensitivity to the type of coloration diffraction imposes is level-dependent; that is, diffraction becomes more audible (and more objectionable) as the level goes up. Those prosound horns that drill your ears at high volume levels - that searing edginess is probably diffraction (and higher order modes - a diffraction-like phenomenon that occurs within any horn, but is worse in some than in others).
So to get back to Unsound's comment, not all horns are created equal, and not all horns are employed equal. In fact, historically low coloration has not been the top priority in horn design, perhaps because knowledge of how to build a truly low-coloration horn was lacking. Dr. Earl Geddes is the leading expert on low-coloration horn design; he calls his devices "waveguides" to emphasize that their function is guiding the sound waves (controlling the radiation pattern), rather than acoustic amplification. The "horn" that I use is a Geddes-inspired waveguide.
Duke