A necropsy at University of California, Davis confirmed the horse died as a result of a gunshot from an unknown caliber firearm, sheriff's Lt. Steve Brown said.
Agricultural crimes detectives and Sonoma County search and rescue volunteers are conducting a grid search for evidence at the scene in east Santa Rosa, Brown said.
The Animal Legal Defense Fund said the shooting happened near Annadel State Park where several horses were in a pasture.
The 17-year-old male horse was named Delta Fox, the Animal Legal Defense Fund said on its website.
"Residents of Santa Rosa have a legitimate cause for concern when criminals are on the loose who could shoot a kind and gentle horse for no reason," ALDF's executive director Stephen Wells said.
The Animal Legal Defense Fund is offering a $5,000 reward for information that leads to an arrest in the shooting.
Anyone with information is asked to call the ALDF at (707) 795-2533, ext. 1010 or sheriff's detective Tony King at (707) 565-2185.
