"It's with sadness we've learned Hawk has been found and had crossed the rainbow bridge. RIP sweetheart," said the post, which has since been deleted.
"The fact that Hawk has been found deceased is enough and out of respect for his family who are mourning his loss, we ask you refrain from asking questions and just accept that he is sadly no longer here."
The death follows that of another miniature horse, Star, which had to be euthanised after being stabbed more than 40 times in a "horrific attack" in Waititi, Otago last month.
Star, a 10-year-old calf-sized horse, was found with stab wounds, including one near the jugular, in his paddock following the midnight attack in the small seaside suburb.
One of the stab wounds punctured Star's bowel and the horse had to be put down despite five hours of surgery. Police are investigating.