Weed Identity / Cover Crop?

I have recently moved to an 8 acre farm about 30 miles SW of Fort Worth, Texas.  The farm recently had a bunch of horses on the property and it looks as if they have completely ruined parts of the soil. 

I have a couple of questions that I was hoping the Permies community could assist with as I am looking to permaculture techniques to bring this farm back to health.

1.  What type of weeds are in the photos listed below...and should I mow them, keep them, mulch them...or just leave them alone?

2. This bare patch of soil was caused by the horses next to a water trough they would spend time at...how would I go about repairing the soil...should I consider a cover crop and if so, what would work best?

Thanks!

Here is the bare patch of soil...

Don't know your weeds, but physical decompaction (rip or chisel plow, backhoe, or till), followed immediately be a cover crop (if you don't soil settles back down in to its previous massive structure) speeds up the process.  Any decompaction is easier if soil is damp (tall order for Texas these days).  Consider cover crops with strong tap roots (mustard family; canola, daikon, maybe legume like alfalfa or sweet clover).. I might assume that the compaction is accompanied by some manuring, so you may have some surplus nutrients that the mustards would appreciate.  Than again it is always good to have a big picture plan and a long term goal before you start investing in a site... maybe this is a pond site?!

Bottom weed could be Solanum elaeagnifolium

http://www.wildflower.org/plants/result.php?id_plant=soel

Not too sure about the first one, guessing something in the Asteraceae family, but that doesn't narrow it down too much

Thanks for the updates and suggestions...looks like there isn't much benefit with the second weed...guess I will just cut and add to the compost pile.

That depends on what you are going to do with the piece of ground immediately after removing them. If you have a plan that's better than what the solanums are doing, then remove them (or chop and drop), but otherwise leave them there - that bit of ground looks like it could do with *anything* growing in it right now.

I have a growing appreciation for solanum weeds. I have some growing in the driest parts of my garden (which impresses me because not much else is growing there) and have been leaving them to do their thing, but often cutting them back before they seed. Chop and drop. I bet your solanums could teach you something important about succession and what is happening with that land. Also see what they are doing in the general area. Weeds often change the soil so that something else can come along, and that's an asset.

Solanums often have poisonous berries, so if you have kids around you will need to teach them not to eat the berries.