Bracken fern

Does anyone have any ideas for removing bracken fern from goat pastures?

I thought goats ate everything !?

In my experience, it's not necessary. If there is plenty of other forage they'll leave it alone. I know some sheep have died of it but my sheep have never bothered with it & I do have tons on my property.

It's toxic and shades out other plants.

The only thing you shouldn't do is try to burn it because it loves to come back after a burn & is an indicator plant for high potash.

Well, A quick web search came up with a few ideas...

Prevention :
Bracken fern spread through spores, which are located under the leaves. When they ripen, the spores drift off like dust and pass through the air or travel in water until they find a good location. The spores cling to machinery, boots and pets that move through infested pasture. Preventing the spread of the fern requires careful cleaning and sanitation, so the spores are not brought to uninfested areas. Machinery may have sections of rhizome in the lower parts that could root and cause infestation.

Nonchemical Methods:
Bracken fern is such a tenacious plant that even fire won’t remove it. In controlled burns, it was found to be the first species to recover. Deep cultivation in the course of 3 years has some effect, because the rhizomes are dragged to the surface where they dry out and die. Slashing removes the green tops of the plants and they eventually starve since they cannot produce carbohydrates. Rolling crushes the growing part of the plant and robs it of energy-producing photosynthesis, but it is not a efficient control.

Cultural / Habitat :
The best way to prevent bracken fern from getting established
is to have densely vegetated land. These ferns are very opportunistic
and maintaining a good ground cover of desirable vegetation
does help keep the spores from germinating.

Manual / Mechanical :
Pulling or mowing bracken fern in mid-summer can lower
vigor by depleting energy reserves. Cutting in early summer,
allowing the rhizomes to regenerate a second crop of fronds,
then re-cutting will deplete the resources of the rhizome much
faster than a single cutting. Mowing will also reduce spore
production, helping to prevent spread, and allow more light to
reach the grass.

And an extension paper. ( as usual it talks about herbicides which are not used in permaculture)
But the other info helps us to understand the plant and may give clues to help fight it, such as it not liking water. Maybe if you irrigate it heavily it might die back?

http://extension.usu.edu/rangeplants/htm/western-brackenfern

Here in NZ bracken root was an important source of carbohydrate for early Maori. I think it requires long cooking to be suitable for human consumption but that might be a way to turn the problem into the solution. Or perhaps pigs would do the job for you.
Also, the fresh regrowth is much less fibrous than old growth so heavy grazing of the new growth by sheep or goats would knock it back. Of.course all the above depends on your bracken being the same plant as our bracken.

Have just checked and our bracken is the same genus but a different species. It's very similar but toxicity is lower which means sheep and cattle can cope with grazing it occasionally. What I read also mentioned the food uses but at the end stated that it is now known to be carcinogenic! Just as well I never got around to harvesting any from the small patch on our place. It is high in potassium though so either chop and drop or cutting and burning then spreading the ash could be useful. The advice is to wear a mask though, ti avoid inhaling the spores.

I think you can pasture your goats with the Bracken Ferns. This is a list from Cornell University Plants posionous to livestock which lists most all of the known plants that are poisonous to goats.

I have been mowing bracken ferns with a cordless hedge cutter. I'm able to cut about 7000 sq ft per hour. I'm sure it will return but with a few more cuttings, my other plants should win.

On the cleanliness issue. Where the ferns are present, spores are produced by the thousands on each plant. Competitive conditions must change. I've got Scotch broom under control. Seeds persist for decades, often with hundreds in a sq ft. Light starvation fixed the broom problem.

Bracken doesn't like to be walked on. A combination of cutting and foot traffic should work.