This is primarily a function of the horn body size and the crossover slope. The steeper the slope and the larger the horn, generally, the lower it will play.

Generally - horn's are highpassed at 500-1300Hz. So, an ID mini horn should be highpassed at around 1-1.1kHz if you have a -24 dB/octave crossover. You can go a bit lower, but that's the recommended range. The full body horns go down to around 700 or 900 Hz, and some custom built horns (i.e. those used in the Speaker Works/Richard Clark GN) go down to 500Hz.

Those are all approximations and generalizations...