I've done indoor sports in low light and flash hasn't ever been an option. I usually try to go early, especially the first time at a different arena, and notice where the light looks best. I try to shoot from a vantage point where the light will be hitting the subjects the most if possible and avoid any dark corners. I see there's a doorway which is bringing in some light, you might think about where you can set up so that light would be hitting the subjects but probably not so you're facing directly into it.
As others mentioned the slow shutter speeds seem to be what need adjusting to avoid getting movement blur.
I'd think about your vantage points and the backgrounds too, sporting events seem to have signs and posts and poles etc. which can really show up in photos and if not straight can be noticeable. The foliage makes for better photos than the parking lot but if you need to get shots from that position then I'd clean up the composition, not cutting off cars and trailers etc. at odd places (and there are some where there's a red box or a red flag on a post along the fence, I'd think about where to set up so you're not getting that sort of a distraction sticking up in your pictures).
I'd think about the timing, the horse and the person leading it and how they're both moving - the ones that look best seem to be where the horse and the person leading it are moving more in sync. Indoors when framing shots I'd try not to get an edge of a doorway in the picture, make sure lines look straight, and think about where the horse and riders are in relation to the blue bunting along the wall.