Yeah, nothing's going to eat that broomweed, except bison or rhinocerous. I'm not gonna go there... :cowboy:
Even if cows graze through it, they'll come up with eye injuries from poking themselves on its stiff stems and branches.
I've dealt with it, too. Broomweed will usually move into an unmaintained pasture around here. The stems are like dowel rods. Right now, I would suggest shredding it short. Then wait a month or two and spray with 2,4-d for winter weeds, because you might get hit by plaintain this winter. Next spring, watch for the young broomweed coming up. Note that young broomweed looks totally different from the mature plant you're seeing now. In its young phase, it's a single vertical stalk coming up, with 2" straight leaves curling out from it. At that point, especially if it's under 6 inches, it's very susceptible to 2,4-d. I'd go pretty heavy at 1.5 to 2 quarts per acre, with a surfactant.
You might need to do a second spraying in late May, to get what the first spraying missed. Beyond that, you'll have to just wait for the spring rains, if any, to bring up whatever grass is there. I nailed the broomweed and ragweed this spring, so I'm keeping cows off my pasture this year, letting the native grass thicken out (which it's doing very nicely) and go to seed. Then after it seeds out, I'll cut it down and repeat the spray schedule described above. I'm tentatively planning to start grazing it again next spring around May or June.
Watch that mesquite, it will consume your land. Spray the trunks up about 24" with a 25/75 Remedy/diesel mix and that will kill them. You didn't mention anything about cedar (ashe juniper), an overwhelming problem on much Texas land.
I agree with some others here that you might have been a little premature putting cows on it at this point.