Another option to the herbicide, and you may laugh, but, get 5-6 goats, to pasture along with the horses. They'll pretty well clean up any unwanted broad leaf vegetation the horses will not eat anyway. I got 2, about 15 years ago to pasture with my horses, and clean up a section of pasture that had a lot of poison ivy, black berry brier's, honeysuckle, and multi-flora rose. Plus some trees stumps that shot up water sprouts in the new fence line. They love that stuff..!! The great thing is, they will browse on it all winter. Great companion animals for "most" horses. I had a Tennessee Walker mare that wasn't too fond of them getting in her space. But the others got along fine with them. Plus, if you hay the horse won't eat. And, depending on the fence you have, or will use, if they can get their nose under it, they will keep the fence line clear.
The Amish in this area that bought old run down, overgrown farms, would bring in herds of 25-30 goats, and turn them loose. Within a couple of years, they had it pretty well eaten down, and made a lot of useful pasture, for cattle, and their horses.