I think this is a good idea. It will give a lot of basic horse handling skills. Throughbreds on the track are a whole other animal that pretty much any other animal out there. That said you are going to see some stuff you don't agree with. The track can be a shocking place for people who are not ready for the mentality and fact that it is a business. I think a groom might be the way to get in the door and it might provide you with good equine experience but I am not sure its enough for a vet school. I would see if you could work with the vet at the track. Grooming is good and you will gain experience but working with the track vet would look better.
If you are interested in the equine tract for vet school. I would look at finding a job working at a vet clinic. A friend of my met with the admissions councilors at Tufts who said they were looking for someone who was working at a practice for a few years and had moved up the ladder and been promoted. I know some mobile equine practices have an "on the road" tech who helps with animal restraint, vaccination preparation, talks to owners and does some billing. I think that would look good on your resume. When you work or shadow a vet and that vet does emergencies let them know you want to do emergencies. This is going to look really good to vet school because it will show that you are interested enough to get out of bed at 2 am to do things. I would also suggest you get a rabies vaccine if you work at a clinic or shelter, most clinics are looking for that even if they don't say they require it.