Some say polos offer a little support, others say they don't at all. When I feel like we're going to be jumping very high or we go cross country, I use boots to protect my mare's legs. But as far as support goes, you want sport boots, they help support the tendon with a strap that goes underneath the fetlock.
I WOULD NOT use polos on the cross country course, as they could easily catch on something or unravel and cause a very dangerous situation! In fact I know in Eventing, at least where I compete, you're not allowed polos on course. Only boots.
"The times when you have seen only one set of footprints in the sand, is when I carried you..."