Consider purchasing "Horse Owner's Field Guide to Toxic Plants". Search online or order from a bookstore. After you review this list, consider what types of landscaping or orchards your neighbors may have. If the property next door has horses too, that doesn't mean the over there is free from names in the list below. Help to protect your horse by checking any area it can reach.
Black locust (robinia pseudoacacia)
Black walnut (juglans nigra)
Brackenfern / Brake fern
Buckeye (some species, but why differentiate) (Aesculus)
Buttercup / Buttercups
Prunus genus and relatives: There are several. Many stone fruits.
Heavenly Bamboo (Nandina)
Kentucky coffee tree
Mountain Laurel (Kalmia)
Oak tree acorns (quercus)
OLEANDER (nerium oleander)
Pokeweed / Inkberry
RED MAPLE (Acer rubrum)
Rhododendron and azalea
Russian olive /oleaster (elaegnus)
And the bright side is there are many other kinds available to grow. Be sure to read a good garden book like the Sunset Western Garden Book to check the genus and common names.