I think the word "great" should be used very sparingly.

I only use it to describe horses who were champions every year that they raced ... or who just missed out being champion to another great horse ... especially starting as a 2YO ... and hopefully going through to 4YO.

By this definition ... Spectacular Bid was the last great American race horse.

There have been some very successful, high-quality race horses since then ... including Mineshaft ... who deserve to be in the Hall Of Fame ... but none to whom I would apply the pantheon word "great."