Trooping the Colour. The Queen used to inspect the troops on horseback side-saddle until some time in the 80s (someone do correct me if I'm wrong on that) when she started riding in a horse-drawn carriage instead. @Donna Hyland
The Queen shot at 1981. The shots startled the Queen's horse, but she was able to bring it back under control within a few seconds. A 17 year old was overcome by police and guards and was arrested and jailed under the 1842 Treason Act.
Horse Guards Parade, 1970, Queen Elizabeth riding her horse Burmese during the Trooping of the Colour ceremony. A Grenadier Guard lies prostrate at attention as all good Guardsmen should when they faint!