In Galiyat, you would meet many locals with their horses offering you rides to near by areas and some time on long routes. Horse ride on short routes is fun but longer routes you need to be extra careful. You can either opt for short routes in Nathiagali or otherwise you have options of longer routes like Miranjani and Mukhspuri peaks. There is a lovely track from governer house to greens spot, you must try it! There is as such no need for special equipment if you plan riding trips on shorter routes. But if you are planning a horse ride to and from Miranjani & Mukhspuri peaks then riding boots, cap and gloves are recommended.
Its fun to have horse ride but in such areas you need to take special safety measures. So do give it a try in your local area before planning for a longer route horse ride in hill-stations.
One thing which is also very specific to this area only that horse owners often as more as they expect more from tourists and also this is the only season when they earn good money. You should have good bargain skills to save your pocket and keep your trip in budget.