This is sad.
However. if I may speculate a bit about why it upsets folks so much.
Most folks aren't used to thinking of horses as wild animals, or animals to be used for consumption. They are both -- just like a deer, wild boar, bears, foxes, coyotes, etc. All are equally majestic, and it's just as sad every time one is shot... But, they are animals. And we are top predators. As long as he didn't torture the mare before her death, then it's just the food chain at work, in my opinion.
That, and provided he didn't violate any laws, then he is within his rights to shoot an animal. I don't like senseless killing - that is, I prefer animals to be shot only for their meat and almost every part of it used, but that is an ideal that does not exist.
Also, as another poster previously mentioned, brumbies in australia are actually a foreign species introduced way-back-when by settlers. They compete with native species, and wreak havoc on the landscape with their hooves. Not saying this makes them deserving of a bullet, just giving ya'll the other side of the coin.