Desensitization?

I'm curious on this topic. What should we expect our horses to be ok with and and what is too much? At home, I like things to be pretty quiet. I understand that show environments are different, but I just want my horse to relax and focus. At the same time, I get her used to Plastic bags, tents, jumps, traffic, tarps, and other miscellaneous things. All of those are pretty typical obstacles to focusing, and Izzy's pretty used to them. (Don't ask about water buckets next to the arena; she finds those fascinating for some odd reason.)

The other day, however, when I was riding, my barn owner's husband came out of the house and started playing fetch with his labrador. The arena we ride in is shielded by trees on two sides, so Izzy never saw the dog coming. She was trotting along and it appeared out of nowhere running at full speed after a ball. Although the dog never left the yard and came in the arena, it was pretty scary for her. A part of me says that she should be ok with dogs running around, but a friend of mine claims that what this man did was both dangerous and thoughtless. Is it too much to ask a prey animal to continue trotting around while it sees it's predator running full-tilt at it?