Benson said this caused a lot of stress to the horses and she wanted it to stop.
"It's not cool, they could easily go through a fence, it's just lucky that no one's been hurt," she said.
So far, no riders had been hurt as previously the drone would chase riderless horses, Benson said.
However, last week the drone approached a pony with a young girl riding it.
Benson said the pony could have bucked off the girl as the drone caused it a lot of distress.
She said the drone had flown to the RDA grounds from Springvale Park and police had been informed about the incidents.
Benson hoped more information was found soon about the pilot as it was making the horses' lives and the role of RDA difficult.
"It's not helping them at all. We don't want our horses flighty, we don't want them flighty for our riders so we definitely don't want them being chased around the paddock."
A police representative said they had received one complaint on the morning of Thursday, May 26, about a drone being flown in the area of the RDA grounds.
Police said the drone was alleged to have flown around various parts of Whanganui, including the racecourse and the RDA grounds.
Police said the complainant was advised to alert the Civil Aviation Authority (CAA).
A CAA representative said two complaints had been received on May 26 and May 30 about a drone flying near the RDA grounds.
The CAA said a person had allegedly been identified as the operator and an Aviation Related Concern (ARC) investigation had been raised by the CAA but not yet assigned.
The CAA has six general rules for flying drones in New Zealand.
They include rule two, which is to fly drones at a safe and considerate distance from people and buildings and to not fly over people unless they say it is okay.
Rule three is to not fly drones over private lands, such as farms or houses, unless the owner approves, and to check with local councils or the Department of Conservation before flying in public areas such as parks, beaches or reserves.
More information on rules and regulations for drone pilots, as well as a full description of the six rules for drone flying, is available from the Drones section of the CAA's website www.aviation.govt.nz/drones
In November 2017 two RDA horses were injured after a group of people got into the paddock overnight and tried to catch the animals.
One horse tried to flee as a man held onto its tail, and another had a boot mark on its rump where it appeared to have been kicked. The other horses were fired up but were physically unhurt.
No one was charged, with police saying video footage posted online was too indistinct to identify the intruders.
