The unnamed rider was involved in a Solihull Riding Club one-day event on Saturday, the club says.
Piggy French wins her first major title with victory at the Badminton Horse Trials, ahead of overnight leader Oliver Townend.
Ros Canter becomes eventing's world number one, the first woman to hold the top ranking since fellow Briton Mary King in 2011.
The National Trust says it had to act due to the risk of "irreparable damage" at Belton House.
Audio & Video
How does blind dressage rider, Nicola Naylor, compete nationally and internationally in para and non-disabled events if she can't see?
Live sport online coverage from the BBC
Check out the BBC Sport Live Guide for details of all the forthcoming live sport on the BBC.
How to get into equestrian sports
How to get into horse racing, whether you want to work with horses at the stables, become a racing jockey or take part in the Olympics.