Hi Andy & Kath,
We did a Jeep excursion into the National Park and they had an option to follow it with a trek on horseback.
I would imagine it could also be done as a stand-alone thing.
It would be fantastic to get into the national park on horseback and our friend Linda who visited us in September has that earmarked as a "must do" activity when she comes back to see us next.
Here's the link again to the Jeep adventure site and Tony organised our trip for us so I feel sure he could speak to them about horse-riding.
www.jeepadventure.it
There's also a riding centre in Belvedere which is part of a lovely new agriturismo and which looks very professional.
We are hoping to find time to make a visit so will report back when we have been but in the meantime here's the link:
http://www.agriturismo-larca.com/ippolita.php
Hope this is useful, Lesley