That could be a tough one. For one, you’re dealing with an era when it was all film, and therefore all negatives. Add to that, the photographer in question, IF he/she is still alive, may or may not have the negatives now.
I went through that myself, for the same period.
There are American Turf books (I think was the name) that came out every year. They listed all winners in races all over the country, large and small. I know the library at Keeneland race course has a set. I don’t know if you can call them and pay for a search or not. If you are close enough to go there, it can make for a fascinating afternoon read.
Then maybe you will get lucky once you have found some specific tracks, dates and races and can contact the track and see if by chance the same group still does the win pictures or not.
Good luck with it.