The Premadasa Riding School is a nice place to learn how to ride horses, swim, and to play badminton or squash. All hidden away in Nugegoda.
Rapidly and messily urbanizing Nugegoda is not where you'd expect to find a stable of horses, but just past the flyover (down Melder Place) there's a track, stables, pool and racquet facilities. It's not a huge space, but it's quite big for the city, and it's full of lovely horses and people to teach you (mostly kids) to ride them.
For non-members a half hour of horse-riding lessons costs Rs. 3,000. For members it's half that, Rs. 1,500. A yearly membership is Rs. 19,000 for adults and Rs. 15,000 for children. That includes horse riding, swimming, gym, badminton, squash and table tennis. They also do swimming lessons.
Regarding just the horse riding, the horses are really nice, as are the instructors. They're not too huge so it's OK for children to ride, and they teach you everything from approaching to mounting to riding the magnificent beasts.
They also have horses and carriages available for weddings and ceremonies.