I am not sure I understand. Do you mean best fencing for horses, as in fields in which horses are kept in? What does stabling have to do with it? Stables are made out of timber or brick walls, not fencing.
A good method of fencing is wooden post and rail with an electrified strand on the top rail to stop horses from chewing. Electric tape also works well. Natural hedgerows are a great fence if you happen to have them and there are also some plastic-type post and rail fences in the market that claim not to break and splinter. Fences unsuitable for horses but used for other animals include barbed wire (the worst), pig netting, strands of unelectrified wire, etc.
For fields, i think hedges are the best. They give shelter from sun, wind and rain and they also allow the horse to browse on different plants.
(must obviously be checked for poisonous plants and holes though!)
post and rail the best, but high cost and high maintenance
we use timber posts with electrified wire (top three strands) bottom two strands not electric. Not suitable for yards, but is suitable for larger paddocks. V safe, if you keep the power (electricity) up to them beacuse the horses soon learn not to touch them - a lot cheaper than post and rails and quicker and easier to put in, easier to maintain
The best I've ever seen are the ones at Cambridge Stud, New Zealand. Every fence is post and rail and behind it is a hedge between two paddocks.
Above the top rail is a netting fence increasing the hight by a further metre. Every rail is covered with fine mesh wire netting so the fence can't be chewed.
Between the rails is an electric wire preventing horses from putting heads through to eat grass on the other side.