Saturn horn sticking

We have a 2000 SL1 that started having the horn go off (continuous, not intermittent beeps). The first time it happened was early in the morning, lot of moisture in the air, and it stopped when I hit the middle of the steering wheel. The second time it happened was during the night (again a lot of moisture in the air) and my son unplugged the horn. Any ideas out there?

Your car likely has a horn relay. It likely is located in the underhood fuse box. Pull that thing.
If you know how to use a voltmeter, check each of the relay’s underhood fuse box connector contacts. One of them will change states from 12V to ground when you press the horn.
If you see that happen, the horn switch is likely working fine and your relay may be sticky. At that point, I’d replace the relay to see if that fixes your problem.
If you don’t see that happen, your horn switch may be sticky.

If it turns out to be the horn relay (assuming your car has one–I had a 1971 Maverick that didn’t), this is the easy repair. However, the fact that you made it stop when you banged on the steering wheel suggests to me that it is the horn switch. If the repair is going to be expensive because of air bag removal, I think you can still get a horn switch that mounts on the side of the steering column. It is connected to the relay by running wires external to the steering column. You then bypass the original switch. It won’t look original, but your car is 12 years old and this may be the easiest repair.