The herbicide label will specifically outline all grazing and harvest restrictions. The Curtail (active ingredients clopyralid and 2,4-D) label found online (which might be different from your specific label) states “Do not graze lactating dairy cattle in treated areas for 14 days after application”. It is common that horses are not specifically included on herbicide labels; most labels focus on lactating or meat animals. When horses are not included, we recommend following the guidelines for dairy cattle.
So, the grazing restriction is 14 days (or whatever your specific label states) for Curtail applied to your horse pasture. Also note that Curtail has additional precautions regarding manure and compost. See the label for restrictions on manure applications from livestock fed herbicide treated forage and for mulch or compost applied to sensitive crops (i.e. soybeans and other broadleaf crops).