You can pan along with moving horses at slower speeds, and maybe get some decent to excellent photos with the 70-300 VR lens. The last horse show I shot was pretty dim...panning was necessary on anything moving, but I had a pretty slow 80-400 VR lens (f/4.5~5.6) and a camera that maxed out at ISO 800 (D2x). Braineack's suggestion of using S mode, or shutter-speed priority and AUTO-ISO will tend to keep the ISO levels HIGH, which would be a good thing I think.
Just keep in mind, if you pan pretty slowly, like using speeds of 1/4 to 1/8 second, you will probably get some neat-looking blurring on the horses' legs and such. The trick is to swing the camera along at **perfectly matching speed** with the horse, which is fairly easy to do at faster panning speeds like 1/20 to 1/50 second or faster. One tip when doing SLOW-speed panning is to let the camera's AF take care of the focusing, and aim by looking right over the pentaprism of the camera...the mirror black-out of an SLR tend to make you pan too fast or too slowly when you cannot actually "see" the target, so this aiming over the top of the pentaprism method actually works pretty well. You might be surprised at how much that bit of visual feedback helps you lock-on and track and swing the camera at the same EXACT speed as the moving target.
Horses look beautiful when panned at slow speeds.
The white balance in the arena might be weird. Be aware of that.