If you want to spray, you will need to identify the type of weed it is so you know what chemical you need to buy. Whatever you do OP do NOT ask the people at lowe's or home depot questions about killing weeds. Call the 1800 number on the bottle and asked someone from the company once you know what the weed is.
There are quite a few chemicals out there that should be safe after 24-48 hours for horses. I personally am a huge proponent of acetic acid (the horticultural variety is stronger than household vinegar). It will kill grass, too, so it should be spot applied.
As I always state, your county extension service can offer great advise and even potentially identify the weeds you are dealing with.
Regular mowing also helps to encourage grass growth and discourage weeds, especially flowering weeds. Rotate the paddocks, mow the ones that are "horse-less" every two or three weeks. If you can keep the horses out of one for a whole year, even better.