be of a great athlete
Antarctica is not a country, as such no.
Any horse with the qualifications can apply for a start, from wharever country they may hail from. This is not the Equine Olympics, the countries do not compete, the horses do.
No country is a part of the IOC that does not compete in the Olympics.
They have to be part of the British Commonwealth
What country does Shaun White represent?
Well you will usually have six gymnasts that will make the qualifications to compete in the Olympics. Then during the qualifications to see who will compete on which event you can have as many as 5 gymnasts but only the top four scores are counted.