I have an easy option but you might not like it......roach the mane off. Tail bag the tail. Get the crap out of the pasture. (I know its easier said than done) by mowing and keeping pasture mowed will keep the weed from going to seed and or spraying the crap to kill it, or hand dig them up. Ugh I know.
Beleive it or not WD 40 does a pretty good job in a pinch to remove the suckers but be sure to wash the mane out completely after its use. Cowboy Majic detangler helps to make it easier to get the crap out and of course baby oil.
"The question is not, can they reason? nor, can they talk? but, can they suffer?" Jeremy Bentham