The horn is a bit of an odd duck.
It is always "hot" (with key on), and a ground gets applied through the horn switch to make it work.
The black wire w/ red stripe is the "always hot".
The black wire w/ blue stripe goes to the switch.
You can test the horn by taking the blue stripe wire off the horn, then shorting that horn terminal to ground.
If it works, the problem is in the switch.
If it doesn't, the problem is in the horn.

I saw this at the harbor freight by my house http://www.harborfreight.com/automotive-motorcycle/horns/2-piece-12-volt-elec...

The price is hard to beat...Any thoughts on this?

I swiped the horns and relay off a junk Taurus, (is that redundant?)
and put them on a little Honda civic. A grown up sound helps. Depending on your needs, looks, economy, ease of installation, there are tons of ways to go at it. Someone recently did a good looking ,dual horn install. I don't know where the thread is.Sorry..
And sometimes a big ball bearing is better than a horn.
I'm still trying to decide if I woulda turned around and followed him and explained to him what kinda bind he put me in . Glad he didn't mash you..

I thought I'd circle back on this to let you guys know that it was the horn that was bad.  The wiring and switch were fine so I just slapped on one of the old horns I had lying around and it's good enough for the time being.  When I get a little free time I'm going to swap out for a dual air horn setup.  I'll post when I do it.

Thanks @youzguyz...Your input surely saved me some time messing with the multimeter.  Cheers!

That's the one. But I do believe they're upside down. You're the guinea pig. And the price of being wrong, IF you are, is low.

That didn't work..

I saw your thread.  Your setup sounds good and looks nice too.  I've done this before on some of my other bikes, hence the surplus horns lying around.  I'm curious about the relay.  On my previous installs I didn't install the included relay, I only installed an inline fuse on the negative wire and they worked just fine.  Please help me understand why you think the relay is needed.  In other applications I've used relays to act as a switch where I wanted to prevent the main switch from arcing and possibly burning out, but this doesn't seem to be an issue on the horn switch on the Savage (or my other bikes) since the switch only closes the positive connection.  It seemed like having an inline fuse on the negative wire would prevent burning out the main switch.  I could be wrong.  If I am, let me know...This is fascinating stuff.

The switch only carries the current to actuate the relay. The small electromagnetic coil. When you push the button, the coil energizes, creating an electromagnet, pulling the heavy contacts together, and They carry the horn current. It's a smaller version of the starter solenoid, same principle.
There's nothing wrong with a work bench mock up. I did one on the Taurus radiator fan I mounted up behind the seat on the backhoe. Let it run fifteen minutes and checked everything to see if anything got hot.
But, in your case, all you need is to identify the actuating connections and the controlled connections. If the relay has four connections, then two of them fire the coil , closing the other two. If six, then hot and ground are controlled. You can wire it however you like. You can ground the horn anywhere and just run the hot wire through the relay. If only a hot wire comes out of the switch and goes to the horn, which grounds to the frame, then, you'll need to create a ground from the frame to go to the control end, so when you push the but on the coil will energize and then when that happens, the heavy contacts close. If you want to just run power through the relay, that's okay. Just tap into a heAvy enough wire to carry the load, run one to the horn, ground horn to frame.