Lived there for 16 years! Plenty of horses in the area with some reasonable hacking ( but some road work required). You can get a permit to hack in Kirtlington Park too - annual fee. Dont be fooled by B430 still a very busy road and cut through from A34 to M40. Grazing - well limited you may be limited but I knew most of the horse people there and many owned their land for their own horses. No liveries but ther is a livery in Bletchington - next door village. There maybe the chance to rent something on the other side of the main road - where there are a couple of Farms but imo to close to main road adn dangerous for crossing and riding along to hack out. Hope this helps. mail me if you want to know anything else