Ask Mr. Smarty Plants

Pyrus calleryana 'Chanticleer' (Chanticleer pear) is one of several cultivars of an ornamental pear native to Japan and Korea.

I could not find any information specific to the Chanticleer pear and the only poisonous plants lists were from Washington State.  On a list called "Poisonous Plants of Washington State" from Cowlitz County Washington, Pyrus spp. are listed and the list states that the seeds, leaves and bark are poisonous to humans, cattle, horses, sheep, goats, swine, poultry, but not to pets. (This seems a bit strange to me that it is poisonous to all others, but NOT pets!)  The poisonous effects are said to be:

"Rapid breathing leading to low and difficult breathing, anxiety, excitement, confusion, headache, vomiting, dizziness, can cause death."

Pierce Conservation District in Pierce County, Washington has a similar list, "Common Poisonous Plants of Western Washington Which Affect Livestock", but have included the Pyrus spp. with the Prunus spp. (apricots, peaches, cherries, etc.) and Malus spp. (apples).

None of the other poisonous plant databases listed below list any Pyrus species, but all or them list Prunus species. Only two of the lists below (ASPCA and Poisonous Plants of North Carolina) show Malus spp.

Toxic and Non-Toxic Plant List—Horses 

Poisonous Plants of North Carolina

Cornell University Plants Poisonous to Livestock

Toxic Plants of Texas 

University of Pennsylvania Poisonous Plants

Canadian Poisonous Plants Information System

So, given this information, I don't know exactly how to advise you. However, I think caution would be the best advice.  If your horse is in the pasture with the tree, you should consider the size of the enclosure and how much natural food is available for the horse.  If there is lots of room with adequate forage for the horse, it probably won't interact with the tree or any of its parts to any extent.  If it is a small inclosure with little other greenery, then it is probably not a good idea for the tree to be there.  If the pear is outside the enclosure but has limbs that hang over the pasture and drop leaves or fruit, you probably want to remove those regularly and keep close watch to see that the horse is not spending a great deal of time in the area of the tree.