No one ever answered this one. My 04 Envoy had this same issue and I fixed it.
#1 Read the OP! The horn works. All the wiring and buttons work.
The steering wheel is not grounded. I can short the horn buttons to ground and the horn honks.
#2 The steering wheel should be getting a connection to ground through the shaft. The one with the big nut that hold the steering wheel on.
See Pic #1
#3 I was troubleshooting, you don't need to take the steering wheel off to do this. You will need to take the cover off of the steering column. I only found 1 screw, seen from underneath.
See Pic #2 You also need to remove the tilt steering lever if you have it. You just grab it firmly with pliers (and something to protect the plastic) and give it a quick yank straight out.
See Pic #3
#4 When I got everything apart I started poking around looking for grounded points. I found this yellow stuff that I think some backyard yahoo added.
See Pic #4
#5 I added a ground wire to electrically connect those two assemblies in pic 4.
In Pic #5 you can see where I hooked it to the upper column. I have a tilt column. There's a small threaded hole there that is used to pull the tilt pivot pin out on that side. It's perfect for this.
In Pic #6 you can see where I hooked the other end of the wire to.
My horn button works now
Note: I added a bonus pic showing the button you push the get the key out of the ignition when there is no power.