Thank you for your tips, everyone.
I have spent some time in the garage today. After a little persuation, the horn button came off.
The investigation this far has shown that the problem seems to get worse when the button is assembled. But it does not dissapear completely.
I'm not good at fixing cars, so digging deep into the electrical system is not really something I want to do.
For the moment I'm trying to elliminate different sources. Last thing I did today was to replace the horns themselves and took the car for a spin without the horn button. No random horns this time.
I'm thinking about replacing the horn button. Even if I can't really verify that it is faulty. To be sure that the button is not the problem.
An as an answer to Spanner Juggler: I live in Södertälje, just south of Stockholm