Why does my car horn goes off randomly?

Last weekend on friday around 7-8 pm, my car horn was going off (as if someone was sitting in my car and holding it down). I had to hit the steering wheel hard to get it to stop, but then it would do it again, and again... It stopped for a while until 4 in the morning. On saturday I took the car and it turns out it needed a new battery, so I got one and had no problems the rest of the week. Until saturday morning. At exactly the same time at 4 in the morning I had to wake up and disable the battery to get it to stop. I finally took out the horn fuse. I have a 2002 Mitsubishi Montero Sport, and I live in AZ so I don;t think this is because of cold weather seeing I have no problems with it during actual winter. An ideas on why this is happening?