I do not think the horn is that powerfull, but that is just my opinion
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Is it the same sensation as when ABS is activated?. If so something is afoot with your ABS (pun intentional) I would imgine, the only electronics that make the pedals vibrate. When you press the horn the car thinks the wheels are locking, it needs hooking up to a T4, suprised it has not blown the fuse.
Does this happen when stationary, if so it must actually be activating the ABS