If the whole soundsystem was a bit more sophisticated doppler-effects should be there automatically in every sound generated. It seems like the horn sounds are not really coming from the car, so there is no relative speed and distance according to the listener to be able to bend sound in the corresponding way. And the fact it's just a sample. EAX effects could easily make doppler-effects out of every audible sound. But that's not really the way to go. It could perfectly be done in software-mode as well. The fact the cars do have doppler is due to synthisized sound that's easily bendable in such ways to sound like doppler.
It still remains that just the whole soundsystem needs to be changed and everything should work fine. It's not just about the horns. And to request horns to be able to generate doppler-effects is not right becouse the problem lies somewhere else. Let's tackle the soundsystem first and we will have our doppler horns for free.