It depends on the type of arena you want.
I have a 100x200 grass arena that is pretty level all ready, so my cost is just the fencing. I am doing wood posts and strapping for my fencing. The strapping comes from FarmTek
. I like the idea of a flexable fence for the arena. I have come off a horse onto a wood rail fence and it did not feel to great. Using these materials and doing the labor ourselves it is going to run around $2000. I can't ride much on it in the winter or after it rains.
If you want an all weather arena with a base and footing it is going to run a lot more. At work we just finished our outdoor jumping arena with 4-5 inch crushed stone base and 2 inch sand footing on top of that and I think the total cost for just the base and footing was around $8,000. But we can ride on it as soon as the rain stops.
On another note, the arena is not the first thing you should be considering when getting a property ready for your horses. You did not say what type of facilities are there already, but first comes shelter and fencing for the horses, and a place to store hay. I have had my girls out at our place for almost a year now and we are just getting around to the arena. I ride in the field where I have mowed where the arena is going to be and out on the trails.