Far too often I see photographs wherein the beauty of natural light is stripped away by the wanton use of portable flash. My advice is leave the flash in the camera bag or better yet at home under your bed! Try instead to experiment with the ISO setting to increase the sensitivity of the camera's sensor to light. I shoot most of my equine photography at 800-1000 ISO. This allows me to capture action in a dimly lit arena or shoot in extreme low light situations such as in a barn or at twilight.
Don't be afraid of grain or "noise" that may occur when shooting. Grain gives your prints an impressionistic or organic feel. I recently had a show of my work at a pretigious gallery on Queen St in Toronto. All of my images were 30x40 inch Giclèe prints and they looked great. Most of those images were shot in very low light at 1600 ISO.
Don't let the camera store convince you that you need a mountain of gear. If you are just getting into photography keep it simple. Don't forget the camera is just a tool to help you record what you see. Don't wreck a wonderful natural image by splashing artificial light all over it.
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Happy shooting, Happy riding!