What areas are you planning on going to and what are your interests? Pretty much every place in NZ offers scenic trek tours on horseback. I've been to Golden Bay on the South Island its really nice, stays warm in late summer/fall and there's a place that offers horse treks on a long sand spit called Cape Farewell, here's their weblink: http://www.horsetreksnz.com/
If you google a place in NZ and 'horse treks' you're bound to find them all over the place if trekking interests you. I think there as many horses in NZ as people so can you be more specific about what you'd like to do here? With the lower NZ dollar horse prices here are also really good so you could go horse shopping if you like as well.