Some of that "NYTimes"  article is true.  There were truck loads of horses turned back at the Canadian border and maybe at the Mexican border. (I've heard both that they weren't and that they were relating to Mexico.)

I have always heard that the Europeans are concerned about ddrugs in American horses in general - not just race horses.  It's common drugs like BUTE that pose a problem.  It may be that the focus has been on throughbreds in some groups, but the problem is universal.  If our horses are in pain, they often get BUTE and other drugs unless they are already at the killers lot where, in my state, the horses are no longer protected by any state cruelty laws.