Planting your fence line with trees and shrubs will certainly add to the beauty of your landscape. As a horse owner myself, I would suggest planting them outside the fence, between the fence and the road.  Horses are great animals, but they can be hard on plants. 

There are some plants to definitely avoid including yew, oak, rhododendron, red maple, black walnut and the fruit trees cherry and plum.  Here is a list of plants toxic to horses from the Oregon Veterinary Association,  10 Plants Toxic to Horses   https://www.oregonvma.org/care-health/equine/10-plants-toxic-horses  with information on the parts of the plant that are troublesome. 

Plants usually considered safe include poplars, hemlock (the conifer not water hemlock), willow, camellia, etc.  This article has additional suggestions, Safe Plants for Horse Pasture Landscaping     https://stablemanagement.com/articles/safe-plants-horse-stable-landscaping-32221?li_source=LI&li_medium=m2m-rcw-the-horse-owner%27s-resource.  I would double check your plant list with your veterinarian, who’ll know which plants cause problems in this area.  

This web site ( Great Plant Picks  https://www.greatplantpicks.org/search/results)is managed by the Elizabeth Miller Botanic Garden in Seattle for plants that do well in our area.  It has lists of plants, like trees, shrubs, etc.  Click on one and it will give you a picture, mature size, best growing conditions, etc.  When you find one you like search the plant’s name and toxicity to horses.  

Finding the best combination of trees and shrubs will be an interesting and rewarding experience.  Start with a few.  You can always add others as you watch the space develop.