The horses in RDR2 are a real pain. You have to make sure to feed them regularly and keep them at a healthy weight so they don't starve to death and literally fall over dead. Most are slow and sluggish with microscopic stamina. A majority are just flat out stupid. The tiniest of predator animals and they completely freak out, throw your ass, and run away. Even if it's just a simple snake. The bears, wolves, cougars, alligators, and panthers I get. But the same panic attack over a snake? The fangs would break off if it tried to bite through the hoof. I've seen it IRL, and know most of the snakes IRL as well. They go low, not high when they strike.
If you want a fast horse with great stamina that keeps healthy (as long as you keep it fed) longer, then you have 2 options. Wait until the stable is open in St. Denis, or head into the mountains. St. Denis sells an Arabian, but there's also an Arabian that you can catch in the mountains. The wild one is the better, and actually best horse in the game (look it up) but also the hardest of all the wild horses to catch. If you want a quality horse, she's worth the stress. Just be stubborn. Her main downside is that she's in the same group as the majority. Absolutely stupid. If you can get past that, then she's well worth the effort. But don't shoot anything if you can avoid it. The gunshot will scare her away and you'll have to leave and come back to try to get the game to spawn her again. There are wolves up in her area, so you may have to leave and come back several times due to having to kill the fucking wolves.