Literally right across the street is Hopewell Farm. The last time I was there, they were standing a gorgeous grey stallion named Skip Away, who won $9 million in his racing career. When I was there they also had The White Fox who is a camera hog.
While you are here, you should also look into some of the Saddlebred Farms. They are generally always willing to give tours(we like to show off as much as our horses do) and most in the Lexington area are just as nice.
DEFINITELY go patronize the Red Mile Race Track. It is a harness racing track. They should be having races in September. The Red Mile - The Red Mile | Kentucky Harness Racing Track
There is SO MUCH you can do in the Lexington Area if you want a horse filled day, week, month, etc. It is a great place.