No more so, I don't think, than any other professional sport.
There are strict regulations, and spot visits to enforce them, on the care, wellbeing, and overall lives of these incredible animals.
I used to go to the track all the time. In all the years I went, I saw exactly one thing which I considered abusive. The horse - a gorgeous, grey filly of amazing lineage - was acting out; pre-race tensions. Rearing and hopping sideways, kicking, bucking even, and just being a handful. The jockey thumped her between her ears. I was outraged. I went to the track authorities, and reported what I saw. They pulled the pre-race tape and it showed what I said it did.
The jockey wasn't even out of his silks before he was being questioned about the action. He was suspended for the balance of the day (and iirc, for the next week, as well...), fined something on the order of $10,000, and the horse was pulled and vetted thoroughly. She was fine, and continued racing the next month. So was the jockey.
Other than that single, isolated episode, I've never seen anything which could be considered abusive. Horses like to run, and if they're bred to do so, they're in their element when in a crowd, reaching for the lead. There is so much money and the oversight is so very tight that I don't see much abuse taking place.
I will codicil my comments to say that the tracks I'm familiar with are large, well known, and "circuit" tracks (on television here in the Los Angeles area), with offtrack betting taking place all over the world. So I suspect it's the top of everything, you know?