As Corinowalk said, footing is very important, but so is size. A round pen needs to be at least 6' high, and IMHO 60' diameter. The 6' height discourages horses from trying to jump it, if you push them too hard, and the 60' diameter is big enough for most horses to lope comfortably in, but not so big that you're running all over creation trying to use it. Material wise, you could use 6' welded wire fence with a 2"x4" at the top only. I would also suggest using a 2"x12" treated lumber at the very bottom to help keep your footing inside the round pen.