Weed control on a budget

When we bought this place, it was covered with Musk Thistle.  I waged a war with that devilish plant, using only a  hoe, and after several years I got them under control.  The former next-door neighbor did nothing with his thistles, and you can imagine my consternation when his thistles grew ten feet tall.  Each year the wind would waft their little dandelion-like seeds onto my place.  
The joke was on me.  Several years ago, for no apparent reason, the neighbor's thistles became fewer each year, finally disappearing.  Turns out some little bug was imported from someplace, a bug that lives in thistle flowers and eventually kills the thistles.  The neighbor, I'm sure, never knew what happened. He probably didn't even notice they were gone. 

Nowadays our main plant pest is this:

It invades our pasture and hay crop.  Mowing does little to discourage it.  There is quite a bit of this stuff growing in our hay, especially in the alfalfa-orchard grass patch.  Because the plant is so big, so thick-stalked, it doesn't cure at the same rate as the hay, and messes up spots in the bales.  Not to mention those thousands of seeds at the top of each plant that creates more such plants wherever we feed the hay.  

You can see how thick they are in places

I told Cliff that after he mowed, I would get out there and pick up as many as I could. He told me to pile them up and he'd take them to the ditch with the forks on the tractor.

This is one of four piles, placed on a bare spot where we fed the cows last winter.  

I was piling some weeds on the other side of the electric fence.  The horses came along and started picking through the pile, just in case I was tossing some good stuff their way.

  
I think I've done all the weed gathering I'm going to do for this season.  
I'm hoping some farmer will come along and tell me what the name of the weed is.  Cliff calls it horse-weed, but I know that isn't the proper name.  I went to Google images but didn't see anything exactly like my weed.  Dock looked vaguely similar.  Could it be dock?