Ask Mr. Smarty Plants

I hope you mean plants, that when eaten by horses, are not known to make them sick.  You will probably have to fence the horses away from these plants as they will probably eat most of them.  I spent several hours trying unsuccessfully to find plants that no horse would eat. But you might check on recommendations in horse forums.  I found several discussions about horses eating plants there.  Horses will also damage the bark of even large trees so you will have to always protect the trunks.

I started by using the Recommended Plants for Ohio from the Ladybird Johnson Wildlife’ Center’s web page. Then I narrowed the choices to full sun and wet soils. (I suspect you may have a low place in your pasture so assumed full sun.)  I then narrowed the resulting list to shrubs and got six of them, then looked for the trees and got twelve.   

I checked each one to see if it was listed in Cornell’s Plants Poisonous to Livestock.  None of these show up there as toxic.

Shrubs:

Betula pumila Bog birch

Hibiscus moscheutos L. Crimson-eyed rosemallow

Physocarpus opulifolius Atlantic ninebark

Rosa palustris Swamp rose

Salix bebbiana Bebb Willow

Spiraea alba

Trees:

Amelanchier canadensis Canadian serviceberry

Betula populifolia gray birch

Fraxinus nigra Black ash

Ilex opaca American Holly

Ilex verticillata Common winterberry

Magnolia acuminata Cucumber tree

Populus tremuloides Quaking aspen

Ptelea trifoliata Wafer ash

Quercus macrocarpa Burr oak

Quercus palustris Pin oak

Salix amygdaloides Peach-leaf willow

Salix nigra Black willow

You can find more information and usually pictures of these plants when you click the links.  And if you need plants for part shade, you can go back and pick the Recommended Plants for Ohio and then pick shrubs and trees that grow in wet soils in part shade.