It seems if you have plenty of acreage, planning is much easier to get, and especially if its for agricultural use. A horse is classed as a domestic pet, and interestingly, if you have room in your garden, you can put up stables for your "pet without permission.
As I keep other livestock, I have a holding number, but I do keep a fair number of ponies too. I prefer to keep my agricultural status, and have never applied for it to be changed over to equine - if I want stables, or a menage, then I would have to do this to get permission - and even after changing, they may not give permission!!
I ride in my fields, and also carriage drive, round cones etc. But I know some people in our area who have been stopped from leaving show jumps up in the fields.
If you only want to graze the fields then don't ask, and unless you are in green belt, a mobile field shelter may be the answer - so long as its open fronted, no hard standing, and you can move it if the council ask.