Hello Donna,
Thanks for taking the time to join us with your memory of your visit so long ago!
It sounds like it is
Deenagh Lodge Tea Rooms in Killarney National Park using the
Killarney Stables for the horses. If you didn't ride yourself, then one of the
Jaunty cart rides. 🐎
Hopefully, this will be the answer to your searches.
What else can you remember from your time with us?