Looking at this, the 12V version provides about half the current of the 5V version - 1A vs. 1.8A
If both the Arduino (800mA) and the horn (600mA) hit max consumption at the same time, it may cause troubles.
Also, if you power the Arduino with 12V, the onboard voltage regulator will get pretty hot.
Have you considered using a boost converter for the horn? This will also provide another layer of isolation.