If your horse is doing alot of hard work (jumping, being ridden more then 3 times a week) id suggest getting shoes just so your horses feet don't become tender and worn from all the hard work he's doing. If your horses feet are strong then he shouldn't need shoes. It all really depends on what work your making your horse do. But if the horses feet are naturally soft and tender I recommend shoes.
In addition to what ginger said, I believe that a lot of arena work does not necessarily warrant the use of shoes. Horses can jump, barrel race, ect. Barefoot, and will actually have more traction that way.
Where you might need shoes. Is if you ride a lot outside of an arena, where terrain can be rough. Shoes are expensive. I keep mine barefoot if possible, but put shoes on at the first sign of tenderness, as I do not want bruises to take me out of riding for weeks.