At international indoor events, flash photography by professionals is prohibited. It can be distracting, or worse cause a horse to shy harming his ability to do his best work.
If you are in the stands, the flash won't reach that far anyway. You are wasting film.
Best results are achieved with good indoor lighting, a fast film such as Fuji ASA 800, or Kodak Royal Gold 1000. A faster film that can be used is Kodak 1600. The lens should have a F stop of 2.8. The best lens for the job is a 300mm 2.8.
The photo shown on the right is an indoor photo without flash taken at S'Hertogenbosch, Den Bosch, The Netherlands, the 1997 World Cup. It is Richard Davison, Great Britain's leading dressage rider in the world rankings.