Any young person of today can hope to ride in their 70s. Whether you succeed is decided by matters outside of your control. Being born under a lucky star helps. However whether you are fit to ride is dependent upon whether you have taken care of your physical and mental fitness and how successful you have been during your life of earning the money to support your riding.
Choosing to compete at the highest level is a very different matter. However some of the most famous names in horse riding were probably in their 70s. My suspicion is that they were born with talent.
PS The best place to watch the equine games is on the TV - getting to Greenwich Park might prove to be tricky.