Chemical Solutions
Roundup is the winner except care needs to be taken, as it's not a selective weed killer, so will also kill the grass. The horses only need to be kept off the grass until the roundup has dried for their own safety, or a bit longer to ensure the weeds are killed.
From the faq - When can grazing resume after spraying roundup brand herbicides?
Proper translocation prior to animal re-entry is imperative to
effective weed control. To ensure proper weed control and forage
removal, Monsanto recommends grazing not resume for 3 to 5 days after
spraying.
- Grazing is safe for the animals as soon as the herbicide has dried.
However, proper translocation must occur before grazing is allowed to
ensure proper weed control.
- When a Re-entry Interval is not listed on
a chemical label, it is recommended to wait until the chemical has
dried, however, assume annual weeds require a minimum of 24 hours of
good weather conditions for proper translocation.
- For perennial weed
and forage control, wait a minimum of 72 hours for proper
translocation of the chemical through the target plants before
allowing grazing.
In Yates products, the chemicals are absorbed by the grass and remain in the grass. The recommendation is to allow the horses into the paddocks after a week, but to mow and tip the lawn cuttings.
To my way of thinking, this is not the best advice, as the horses can graze on the grass as it grows and ingest the chemicals. I'd keep the horses off the pasture for 6-8 weeks, then mow and discard the clippings.
.../ is a great product for lawns we don’t really recommend using it
for pastures. You’ll need to keep the horses off the grass for at
least 1 week and a mow where you catch the clippings and remove them.
The advantages of such products is, they are selective herbicides and will not kill the pasture. So it can be easier doing a large weed infested area, without fear of killing any remaining grass.
Grazon is recommended by many horsey people, but I haven't found information supporting or denying this.
Alternative Solutions
Boiling water will kill weeds - in fact it will kill any plant, so care needs to be taken to pour it on the weeds only. This can be a tedious and time consuming process for weeding paddocks.
Vinegar sprayed onto weeds in the sunlight will also die. Once again, it will also kill the grass, so care needs to be taken with application. The horses cannot be allowed to graze while the plants are damp. In fact it would be better to wait for rain, but that is being cautious.
Iron Sulphate and Ammonium Sulphate. Wet the weeds with and iron sulphate (in a solution) and dust with the ammonium sulphate (in crystal or powder form). Let it sit for 3 days then hose it in. These chemicals can also act as a fertiliser, so are relatively harmless.