Thanks all who had troubleshooting steps... I am afraid the circuit has just gone bad and I'll have to have someone out to repair it. I have turned the breaker OFF on that, I still have lights out there, we've rigged the fence charger to a different outlet on the good side of the barn and we'll get by. I have another electrical job here in the house to do too, so I'll probably just break down and get a guy out here.
Just for grins... here's where the wiring runs, if you can see the wires on the top of the second 2X6 from the roof. In the first pic... There's the dead outlet near the pony's doorway, and the fence charger now connected with the extension cord to the other side of the barn that still has power. It's all high overhead, but exposed so you can see it most of the way around the barn. It ~was~ at waist level, and my dad moved it up high this last fall when we re-modeled the barn to make the doorways. When we raised it, there was extra length to the wire and we just made a big loop (second pic) you can see just to the left of the outlet.
The horses... seem to have relaxed some and were eating hay again in the lean-to. Pony's the one over there near the doorway. Bay nearer.
Bay ran pony out and went down to that hay rack... and now Cyn is coming in.
Their behavior this morning was likely unrelated to this electrical issue, and perhaps was due to some other animal or something in the woods. I just may never know.
Just read through the posts on your barn. I'm not trying to alarm you, but just want to mention a couple of things.
As RoS said earlier, I'm an electrician, and the first thing I would do is kill the circuit (which I see you've done). Get someone knowledgable about electrical stuff to check the circuit and find the problem. It could be a loose connection, or a rodent chewing through the cable (they sharpen their teeth on the metal).
Another thing to check is for the smell of smoke, or anything that's warm that shouldn't be. (I'm also a volunteer fireman). I once got a call to a house that had been burning (smoldering) for three days before anyone noticed.