If the horn is electromechanical with a coil and interrupting
switch, that's going to constantly generate flyback voltage
excursions across the coil. Many old buzzers were that way.
Think of them as relays with the NC contact controlling coil
power. Set that up and you'll hear the relay arm buzz.
Maybe if you cut power by this alleged MOSFET at just the
wrong time, its now-open-circuit drain might leave the coil
flyback energy noplace nice to go, and punch out the FET
gate (D-G breakdown).
Or maybe repetitive avalanching is not something the FET
is built for (avalanche rated is a special feature).