The best method for an amatuer photographer to take professional quality photographs of horses... is simply volume!
If you take enough pictures, from enough angles, with enough differernt settings, you will eventually get a fantastic picture.
I adore this picture of one of my mares. I love the lighting effect, love the background, love the place she's at her her stride, love the expression on her face. Guess how many pictures I took that afternoon trying to get the perfect shot...? just over 300.
But it took less than 15-20 minutes to take all those!
What you really need in order to get fantastic horse pictures that capture a "moment" of action not just a posed horse is a huge memory card and a constant "burst" mode. Burst for some cameras means it will take 3-5 pictures one right after another-Some- even lower end- cameras will take several pictures a second as long as you hold the button down until the memory card is full! With this method you can take about 20 pictures in the time it takes a horse to approach, jump, land, and canter off after a jump- ensuring you will have captured the perfect horse action shot.
When I take portraits, instead of waiting for an ear to flick perfectly forward and fumbling for the shoot button, I just hold down the button and the camera starts firing shots so when something pricks the horse's attention, there's no doubt I captured the moment.
The camera I recommend for this method is a Canon PowerShot A530. It's small enough to keep in your pocket to capture the occassions the horses decide to show off, affordable enough to expose to barn life, but very powerful as well. This camera has a fantastic burst mode, but keep in mind a camera can onlytake pictures as fast as it;s card will allow it to save images. To get the best performance you'll need to buy a high speed card, the larger the better. The card you need to take enough pictures to shoot continuously is the 1gig san Disk Memory card or the 2gig SanDisk Memory card. I recommend the latter, as a 2gig card allows me to shoot several hundred pictures, then film a extended video segment without running out of space. Both come in very handy doing sale horse videos and photos.