Cheap horns will probably be worse, the problem is horns have a vibrating contact which creates back emf, Rf radiation, spikes and various nasties, even air horns have a compressor that will generate junk, but you should be able to deal with it Ok.
Put the diode and 100nf cap / 100 ohm resistor as close as you can get to the horn, on the horns terminals is best, you need to kill the electrical noise at the source.
This is a class x cap, basically its designed for noise suppresion, class x means its rated for mains, we dont need that, being designed for noise suppression we do need:
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I odnt have schem tools on my works Pc, the diode is so if the 12v vehicle side drops down low enough to reset the chip then the diode disconnects the supply temporarily and the cap powers the chip for a few mS, a diode inline with the smps you have will probably work, as it no doubt will have a large cap on the input side.
If you monitor the battery at its terminals you might not see it, you'd need to monitor the power to the processor, and even then if you use a 'scope it would need to have enough bandwidth to detect any hf noise, it could be though like you say radiated Rf noise causing the issue, the 100nf cap and 100 ohm resistor will dampen Rf quite a bit.
Your not old enough to remember points ignition!, maybe I'm too old, points ignition is from way back in the 70's, ignition system used mechanical contacts in a dizzy or ditributor to switch the coil on & off, they like the contacts in your horn sparked and generated lots of noise, the condenser was to resonate with the coil controlling the spark at the spark plug and reduce flash at the contacts.