The dogs behaviour was witnessed by the owner of the Mosston Rd land Ms Glasgow grazes some of her horses on.
He told her they were a brindle mastiff type and a "little, fluffy, white thing".
The landowner noticed the two dogs harassing about four of five horses, and chased them away, having to defend himself when the smaller dog ran at him instead.
"He hit it with a pile of s---," Ms Glasgow said.
But while the dogs left the first group of horses alone, they carried on down Mosston Rd to another block of land where Brave was grazing.
The owner of that block discovered Brave lying in a pool of blood, with one of his legs "wound up" in the wire fence.
"It's down to the bone ... it's still touch and go whether he's going to be sound. If it's unsound, he'll have to be put down. He will not be a show pony from now on; he's too scarred up."
If Brave's leg was sound, he could be used for dressage, jumping, or being someone's pet.
Ms Glasgow called Animal Control and said they told her the other man shouldn't have tried to chase the dogs away, but should have instead monitored the situation while waiting for dog rangers to arrive.
She understood the reason, but believed Animal Control didn't understand the position they were in when they needed to protect their horses.
Animal Control team leader Jo Meiklejohn said they told Paula if an animal was being annoyed by other animals, the owner had the right to protect them by chasing them off, but notifying Animal Control immediately was the best way for them to try to identify the dogs.
"We are sorry to hear about Paula Glasgow's pony and understand this isn't a nice situation," Ms Meiklejohn said. "Paula contacted Animal Control two days after her pony was chased into a fence."
Ms Glasgow said neither she nor the man had contacted Animal Control when the dogs were first chased away, because she felt Animal Control was never any help.
She said she had called "countless times" in the past about dog issues, and "not one phone call had been put into their system".
Ms Meiklejohn said there was one call from Ms Glasgow recorded since October 2014.