why did my horn blow?

Just depends on how much you like the new car smell versus a swamp smell. If it were me I'd try to keep the weather out as much as possible.

Sometimes after a hard rain I come out to my TJ and the radio is on and playing. (Reminds me of the movie Christine). Its kinda of wierd but im asssuming the same thing is happening with your horn. After it dries out its usually fine. You should look into a rain gear cover, if your going to keep the top and doors off. As for damaging your interior. It will get sun faded if left out too much, and your carpet with stay wet for a while causing the "swampy" smell. Other than that I doubt it will hurt much although i did fry a turn siganl fasher once after a hard downpour. I removed my carpet and keep the drain plugs open, as im lazy and hardly ever put my top on in the summer.

Jeeps, especially the newer ones are far from waterproof.

Unless you want to have lots of electrical problems down the road I'd try to keep it as dry as possible.

2x on the Rain gear cover.. Mine is 3 years old and still doing the job. Nice heavy canvas. Use it the entire Spring/summer/and fall. until its time for the soft top again.
Had to spray Water proofing on it once.

http://www.jeepcovers.com/

They are the only ones that make a CJ8 cover as well. Also like how they cover the door area.. Keeps all that dew out. for sure.