Apologies if this is answered somewhere but I've searched around and haven't been able to find anything. I'm wanting to know if there is a way to tell when you have a good horse. From what I understand, each territory has a rare horse type that you can tame. After doing the horse breaking quest for Bonnie where she gives you your first horse there was a popup that said something along the lines of "Your horse is rare/fast/agile/badass." I think it was called a Kentucky Saddler, but I could be wrong.
 
I kept that horse all through the first territory and into Mexico and it always seemed like a pretty solid horse. Then I did one of the horse breaking side missions in Mexico and my horse (the one that responds to the whistle) changed from the badass Kentucky Saddler to the crappy horse I broke in for the mission. Since then I've been breaking wild horses trying to find the next equivalent of the rare Saddler, but I can't find any where in the game where it tells me what kind of horse I'm on or what the quality of said horse is. I'm assuming if I found the rare Mexico horse I'd get another of those popups like I did when I first got on the Saddler, but I could be wrong.
 
Any tips on taming quality horses? I haven't beaten the game yet so please keep replies clear of plot spoilers. Thanks!

You will not get a pop up. But I can tell you WHERE to get a nice horse.  
 
Any of these three are great  
 
And a bit about each 
 
American Standardbred  
Kentucky Saddler *Which you get from bonnie* 
 Hungarian Half-bred (Which is needed for the "Heading South on a white Bronco" Trophy/Achivment" )
 
  

compare the horse you have to the descriptions at shops

Awesome, thank you

Yeah, like the pages linked to above say, those are the three best horses in the game. The jet black horse, or "American Standardbred" is the fastest, yet most vulnerable to damage. The white horse with the black nose, or "Hungarian Half-bred" is the least vulnerable to damage of the three, but it's the slowest of the three, as well. Then there's that palomino called the "Kentucky Saddler", the one you got in that early Bonnie MacFarlane mission. It's not as fast as the first or as strong as the second, but a well-rounded mixture of the two. Thing is, horses die pretty easily, no matter what. Just buy a deed to your favorite of the bunch and you won't have to worry about its health. (Mine's the Saddler.)