Good luck trying to use flash at 8 or 10 fps! It simply won't work with most flashes. You'll have to slow down. If you use fill flash, you might be able to get two or three shots off before having to pause while the flash recycles. With full flash - where the flash discharges more completely and nearly always needs to recycle - you'll probably be shooting one frame at a time. That might not be a bad thing... there's often little to be gained by cranking out 8 or 10 fps, other than a whole lot more pictures to edit at your computer at the end of the day.
With the bigger external flashes (550EX, 580EX, and I think 430EX and later), you can add a supplementary battery pack to force the flash to recycle faster. Canon has their CP-E2, E3 and E4s, that put a bunch of additional batteries at the flash's beck and call and will help. Using rechargeables in both the flash and these supplementary battery packs will also improve recycle time. Or there are even bigger and more powerful third party battery packs (Quantum, etc.)..
HOWEVER, with all these additional power sources you risk burning out the flash tube (Canon probably has a safety switch that shuts the flash down before that happens, as a precaution... I know for certain they do on the flashes built into the cameras.) The batteries themselves heat up, too, with heavy use. I use a few CP-E3 and E4 and they do get a bit warm to the touch, after a longer series of flash shots.
Flash will give the best results in a lot of cases. Even if you get über fast lenses, you simply will start to bump up against new problems with too shallow depth of field and heavy shadows, both of which only a flash can solve for you (higher ISOs can't help with shadows, either).
I'd use flash sparingly and mix/supplement it with ambient light shots, as necessary and possible. Look for brighter and more shadow-free areas within the arena where you can do without flash. Alternate shooting there and with flash elsewhere.
I shoot equestrian and sometimes use flash. Many indoor equestrian arenas are damned dark. Some have ugly sodium vapor or mercury vapor lighting (which I ask to be turned off, whenever possible). When it comes to flash, horses very rarely even notice... Occasionally less experienced riders or trainers (or parents) fret about it, but I can only think of a couple instances in many years and many tens of thousands of shots where it's actually been a problem. Nearly always it's young, green horses, so I watch out for those and avoid using flash around them.
It's particularly a no-no to use flash at dressage events... usually. Yet one of the biggest dressage facilities in California has their main arena pre-wired with a bunch of strobes that the "official" photographers can use. So there's a difference depending upon the level of competition... at national and international levels, flash is accepted. It's at the local and more amateur level where it's frowned upon.
I don't know what cameras are being used, but newer models can be better about noise. The original poster of this thread way back when was shooting with 40D... 50D didn't improve much on that (it had similar noise levels and high ISO performance, but with 50% increase in resolution). 60D and 7D certainly did... Offering about a stop higher usable ISO. 5DII's AF is generally too pokey for this type of photography, though it offers yet another stop higher usable ISO. 5DIII and perhaps 6D would be better, about the same high ISO performance as 5DII in RAW, one or two additional stops with in-camera JPEGs, and AF systems that can keep up with action (and are more low light capable). If your checkbook can handle it, 1DX would be fabulous, lower resolution FF equals ultra high ISO capabilities.
For ambient light shooting, you also might look into noise reduction softwares, if not already using something, that allow you to shoot at higher ISOs.
EDIT: Yes, definitely shoot RAW! That will help. RAW files have so much more latitude to make adjustments. Using a RAW batch processing program like Lightroom, you can easily add some "fill light" too, that helps immensely. It's still important to get good exposure. Avoid underexposure like the plague... any time you have to increase exposure in post processing you will amp up noise even more. It's usually better to slightly overexpose, eve use a higher ISO in spite of add'l noise it puts in the image, then reduce exposure slightly in post processing and, if necessary, do some additional NR work on your selected images. Just do the NR work before any final sharpening.
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