This isn't construction advice, but here are some free advice tips on design for equine safety and behavior. For equine soundness, you want the round pen flat, level, and with enough sand, or rounded pea gravel but not too much. Pea gravel drains much, much better, and doesn't compact much to speak of. If you end up with tenderness in the equine soles, then there are farrier / stall footing issues. Having all of your loafing areas in pea gravel will help toughen up he soles. If the round pen footing gets deep, you run the risk of torquing/tweaking tendons, especially with young or high strung stock, which are usually the ones you have in the round one anyway. I would also point out that a larger diameter pen is better, as it keeps the turning forces on the horses lower. Finally, if you can, make the walls solid all the way up to 6-7'. It will help enormously when training as the horses will be much less distracted by motion outside of the round pen.
Definitely put a solid 18-24" of 2x at ground level as a "kick board" to keep your sand and gravel in the pen.
Yes, we do all of our own hoof care and have done so for close to twenty years, while putting on tens of thousands miles on the trails with our equine companions. Keeping horses sound is a big deal for us.
All the best,
Peter