http://www.colorpilot.com/comp_rules.html
Composition for riding? Horse portraits, landscapes, people? There are tons of composition "rules" some of which don't apply in every situation. Here's a website with a bunch of articles. I wouldn't take anything as gospel, but it shows a lot of opinions and examples.
http://photoinf.com/
Big things...
Rule of Thirds- Basically it breaks up the imagine into thirds both vertically and horizontally, making 9 boxes, and four intersections. The eye is naturally drawn to these intersections and placing what you believe to be important on one of these interesections draws the viewers attention to this point and it makes for a more natural balanced image.
Like here -
http://phyxius.smugmug.com/photos/174612426-M-1.jpg - if I divided the picture into thirds vertically a line would be going through Dougie.
Diagonals- Diagonal lines fill frames, but also offer something different for the viewer.
http://phyxius.smugmug.com/photos/168982841-M.jpg
Fill the Frame -
Noone wants to squint to try to see the subject. Fill the frame!
http://phyxius.smugmug.com/photos/173431260-M.jpg
Room to Breathe -
Kind of in direct contrast with the above, you want to allow certain objects breathing room. For example, if you're photographing a horse in motion you'll want to make sure that the horse has room to move, so that he/she doesn't appear "trapped" in the frame.
http://phyxius.smugmug.com/photos/129551196-M-4.jpg
Sports Photographers usually subscribe to the theory of shoot close, crop closer. With horses you generally DON'T want to do that. Some shots are wonderful cropped close, many just look cut-off or un-planned.