Weeds in the fencerow

The neighbors' horses have a habit of leaning over the barbed-wire fence and eating on our side of the fence.  This is the nature of horses; they all do it, whether well-fed or starving.  Barbed wire doesn't deter them in the least.  They'll push the fence down as far as possible and stretch out their neck as far as they can reach, eating all the grass they can get.  If a barb happens to rip their skin open, they don't even let on that they feel pain.  
Last summer, to keep our fence from being totally torn down, we put an electric wire along it in a place where the horses would get a shock whether they reached over or through the three strands of barbed wire.  All it took was one shock apiece and they stopped.  
Late in summer the weeds overtook the electric fence, shorting it out.  Cliff figured the horses wouldn't know the difference, and they didn't, at first.  Eventually, though, they tried it again and found out it wasn't going to hurt them.  
I told Cliff yesterday that we'd better get the electric fence working again.  

The trouble is, those dead weeds will all have to be taken out or they'll short out the fence, just like last summer.  After Cliff went to work, I went out and started taking care of the weeds.  It's tiring work, let me tell you.  

On the neighbor's side of the fence no grass grows, only weeds.  I do believe they feed their horses though; in fact, from the looks of them, they overfeed them.

This is one of them, last time he got out and ended up in our yard.  Again.  

Here's what the pasture on our side of the fence looks like.  Plenty of grass. 

You can see how far the horses have reached over and cropped the grass on our side.  I'd say about three feet.  
The aggravating thing about this is that the neighbors take no responsibility.  They won't help with the fence.  If we had to put new fence up, we'd have all the labor and expense.  Let's face it, they won't even fix their fence well enough to keep their horses at home; they're sure not worried about this fence.    
And you have to wonder why they keep the horses; they never ride them.  
Oh well, such is life in Dogpatch.  
I got about a tenth of the weeds pulled and stomped down today; I'll do more tomorrow.