It is well-established that horses bedded on wood shavings that contain 20% or more black walnut shavings can develop the hoof disease laminitis. ... However, a hungry horse that has little to eat except walnut leaves, fallen walnuts, or branches that have fallen into the horse enclosure may be at risk.
Don't know about gardens but back in my days working as a farrier's asst I remember my boss telling owners to get rid of all the walnut husks and leaves in the pastures. Do not put anything from the walnut tree around your horses.
Walnut trees in New England are no where near as common as they are here on the Piedmont. Still it was a concern back in the 1970s.
Here some walnut from Hurricane Fran. Air dried.
No horses were harmed in the creation of this piece of art!