It is still not known who owns the string of horses roaming the area, which is also popular with walkers.
It is thought up to 20 of the animals, the youngest of which is thought to be around one year old, have been left on the park land.
The council have appealed for their owner to come forward and said they want the horses off their land.
It is expected that the animals will be sent to Crosskennan Lane Animal Sanctuary, which cares for abandoned horses. But Lyn Friel from the sanctuary said moving the animals is not straightforward.
"Some of the horses can be handled, some cannot, and they're in all different areas. We've been up days when we can't find them, or when they were not all together.
"It's also very difficult conditions as they are on the hill in uneven ground, and it's difficult to get a horsebox up there," she explained.
The horses appear to be in good condition but Lyn added that they will need help in the near future.
There's enough grass to sustain them, but in a short space of time they will be in trouble.
"Some had injuries that were healing nicely, ones that you would find in stallions running together - bite marks for example."
A horse expert is expected to come over from England to help with the move from the land to the animal sanctuary and a council spokesperson said, "We are working to ensure that the horses will be humanely removed from the park within the next few weeks.
"There is no question of the animals being destroyed," the spokesperson added.
The horses will be expensive to keep and Lyn said the animals will need long-term re-housing, but that could be difficult - especially with the current increase in abandoned animals.
"People do not want horses that aren't broken in for riding," she said.
"Our phone is going every day of the week. We need to indentify more good homes where people are willing to take them on."