There are many royal ladies who really got into riding a horse rather than their husbands (Kathy Griffin wrote that)...Whether in ceremony, competition, for sport, or for pure enjoyment, many Here's a collection of past and current royal, and noble riders.
1863, Queen Victoria with John Brown, her Scottish servant/companion
Marie Antoinette riding in the royal Hunt, 1777
Queen Margarita of Spain and Portugal, 1634-35
Empress Elizabeth of Austria
Queen Beatrix, the Princess Beatrix
Queen Elizabeth and Princess Anne, 1981
Princess Anne at Windsor Horse Trials, 1972
Zara Phillips, cross country
Camilla Parket Bowles riding in the Beaufort Hunt, 1997
Princess Nathalie at the 2008 Olympics
Charlotte Casiraghi show jumping in Valencia, earlier this year.
Athina Onassis de Meranda
Athina and Charlotte
And here's the biggest joke, not even riding her horse