Bring several powerful off camera strobes. Indoors with the T3 and a kit lens will be some tough shooting to get sharp vivid pictures. Even with a faster f2.8 lens you still would struggle with the T3 in this light. The Great Smokey Mountains Expo Center is an indoor horse arena and not lit very well for photography so you would need off camera lighting to get the pictures you described. Depending on how close you can get to the individual parts of the actual track you coul get away with one off camera remotely fired speedlite.
If you can't use off camera lighting, your best bet is to try and find one spot on the track directly under one of the "high" overhead lights, establish what you exposure will be, and prefocus waiting for the riders to hit that spot. Keep your shutter speed as high as you can so you can stop the action or try panning to at least keep the riders face as sharp as you can. Good luck and have fun at the Volunteer Nationals..
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