Hair Sheep for clearing Ragwort Tansy?

Greetings!  Does anyone have experience using Sheep to eliminate Tansy Ragwort (Senecio jacobaea)?
The pasture has been continuously stocked with horses for decades, and now there is a huge population of Ragwort.
I'm pretty sure they are saying, "enough with the horses already!"  

There is a population of Cinnabar Moths whose larvae eat it and Flea Beetles damage it, but not significantly enough.
It can be pulled when the soil is wet (and makes good mulch) but there is too much for that. And each pull makes a bare spot that the rootlets and seeds recolonize. Mowing causes it to perennialize and make even more seed.  
I have read that if the plants go to seed they will die, and if the soil stays undisturbed the seeds will not grow.

They are lovely plants useful traditionally for removing tumours, etc... and they cool the soil beneath by their shade, but...
They are toxic to most livestock and dominate the pasture thoroughly.

I have read that Sheep will eat them to oblivion without ill effects to their own livers.
I don't want to have to shear wool, so Hair Sheep appeal to me.

Does anyone have experience in this particular situation?
Any Hair Sheep breeds better than others at foraging this plant?
How many sheep would I need to effectively work a 5-acre area?
Also, blackberries and thistles in abundance.
Thank you kindly for any help.

Ragwort IS toxic to sheep they are just not quite so sensitive to it as horses and tend to have much shorter lives so that the liver damage does not become so obvious. Personally I wouldn't graze anything on ragwort. I dig up all of the rosettes and put clover seed down in the bare patches. I rarely see it on my land these days.

Thank you Katy for the helpful knowledge and experience.  That makes a lot of sense, occupying the bare spots to thwart Ragwort recolonization. I will give the clover a try.
I will wait until the Ragwort is much reduced, and the pasture improved, before I get some Sheep.
Thanks again.

Ragwort tansy is bad news for sheep but I've read information on someone successfully grazing out common tansy with Katahdins.  They measured blood levels and found no increase in toxicity but again, that is common tansy, not ragwort.  I will see if I can dig up the website with the info...

I have found my sheep will graze on a long list of weeds that are considered noxious to them. To actually graze something out of existence though takes mob-grazing and that is where you could run into trouble.

As for blackberry, oh they will graze that out of existence. I had a prized area of raspberries that had been in the family for many generations and grazed it out of existence accidentally in about 1 weeks time. I have purposely grazed poison ivy out of existence in about 20 minutes mob-grazing a patch (its a sheep's favorite food). They are pretty resourceful manias, and as a whole, if you put sheep on a pasture long enough they really make it a great one.

As for hair sheep, I had them and never will again. Considering their low prices at auction, their smaller carcass size, their shortened back which gives less chops, and their flighty behavior, I will GLADLY pay the $6 a head to shear them and make an extra $40 per head in meat production to boot.