I am looking for a camera for around $1000 to take action shots of horses. The horses would be moving around 20 miles per hour.
I think it's got more to do with the setting than the camera. Any good SLR for $1000 should do the trick.
I think a general answer would be: - any camera that can focus fast (so point-n-shoot is not likely an option) - a lens to go with the dSLR that can focus fast (some cheaper lenses may still give you some "lag") - a lens with enough "reach" (focal length) so you can visually see the target subject without it being too small; so you may want image stabilizer if you are at long focal lengths - a camera with a frame rate that is fast enough to capture multiple frames per second
So for example (since I am a Canon shooter, I can only recommend what I know), a good starting camera setup would be: a Canon 50D or 60D or 7D paired with either a 24-70/2.8L or 70-200/2.8L IS lens
NOTE: a lens that has an opening of f/5.6 or smaller (higher f/stop number) could cause your focus lock to take longer and given the horse is moving, you may miss the shot
This is only my opinion of what I'd recommend.