You could use 2,4 D instead (Crossbow). This will work on broadleafs but not grass. Some horse owners have reported that horses that lick Roundup can get colic. For 2,4 D, there are no restrictions for horses on pasture, but you should spray when plants are actively growing (not during hot drought), using 4 quarts per acre broadcast sprayer or 2 ounces per 1 gallon spot sprayer.
Roundup can be used as it has a relatively low toxicity as long it is applied according to directions. It should not be allowed to puddle, just like any other herbicide.