The horses were used in an educational and therapeutic programme for people with disabilities, and had to be carefully trained before it was safe for them to ridden by the clients.
Stevens said it was possible the horses might not ever be confident enough again to be included in the programme, which would be a heavy blow to the charity.
"It could be that we may have one or more horses that may not have the confidence to allow anybody back on them to ride them," Stevens said.
One of the horses had stiff back end and the other one had some damage in the front and was walking slowly as if it couldn't stretch out its legs.
"It's dragging itself in the front," he said.
"The other horses were fired up but physically they're okay. What's going to happen when it's night time again tonight? We don't know. When a horse gets scared its natural instinct is flight. We don't need it running on to the road, we don't need it smashing into fences."
Stevens questioned the mentality of the people that would do such a thing.
Video of part of the incident was posted on social media last night and shared to Stevens.
"Some wally plastered them up on Facebook."
The video, taken from SnapChat, shows people approaching the horses and trying to catch them. At one point a man appears to cling to the tail of a fleeing horse before falling to the ground.
Facebook users have provided names for some of the people in the video, which have been passed on to police.
"All we know is that they are under 20 years old and known to the police."
"The support from the community has been incredible. A lot of people have affiliation with these horses and have known them over the years. People have been ringing up who are previous or current clients to find out who they are."
The therapeutic benefits for disabled people riding the horses was "absolutely incredible", but thanks to the injuries caused to the horses some people might miss out on rides for a while.
Stevens was "gutted" about what had happened, and called for the people involved to go the police station and confess what they'd done.
He then wanted them to come for a visit to the charity and see what they did, "to show what they potentially could be destroying".
Head coach Wendy Sellars said she was "madder than a snake who has been poked with a stick" after finding out about the incident.
"The RDA is not a public place and the horses are not public property and are expensive.
"It is not okay for people to trespass or interfere or hurt the horses."
A police spokeswoman confirmed police were looking into the matter.
