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.
Avocado
Black locust (robinia pseudoacacia)
Black walnut (juglans nigra)
Boxwood
Brackenfern / Brake fern
Broccoli
Buckeye (some species, but why differentiate) (Aesculus)
Buttercup / Buttercups
Butternut
Castorbean
Prunus genus and relatives: There are several. Many stone fruits.
Chestnut (Aesculus)
Chinaberry
Dutchman's Breeches
Elderberry (Sambucus)
Fiddleneck
Foxglove
Goldenchain tree
Goldenrod
Groundsel
Heavenly Bamboo (Nandina)
Holly
Horsetail
Hydrangea
Jimsonweed (Datura)
Kale
Kentucky coffee tree
Lambsquarter
Lantana
Larkspur (Delphinium)
Ligustrum
Marsh marigold
Milkweed
Mountain Laurel (Kalmia)
Oak tree acorns (quercus)
OLEANDER (nerium oleander)
Pigweed
Pittosporum
Poinsettia
Poison Hemlock
Pokeweed / Inkberry
Ragweed
RED MAPLE (Acer rubrum)
Rhododendron and azalea
Russian olive /oleaster (elaegnus)
Skunk Cabbage
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.