Riding Club Championships is a free to play app on Facebook, where you can train your own horse and compete against friends and players from all over the world in this beautiful 3D game. Ride your virtual horse over beautifully designed varying obstacles such as, oxers, uprights, Liverpools, spreads and more. You can even create, decorate and ride your own courses!
Source: The Riding Club Championships wiki.
Originally released in 2007 as a downloadable game for Windows with a monthly subscription fee (after a two hour demo period), the game became free to play in 2010 before being relaunched on Facebook in 2011.