You can review your horse's stats by accessing Menu > Player > Horse. To see the stats of horses you don't own, get near the horse or use a binocular. It's recommended to study an unknown breed to add it to your compendium and to see its stats.
Stats vary, even among horses belonging to the same breed. Finding a rare breed, with elite handling, and high default stats is an incredible find. If you ever happen across one, don’t let it get away and steal/tame it at all costs. Fortunately, there’s a method of getting these end-game horses as early as Chapter 2 and will only require a lot of saving/reloading, depending on your luck. You can check it out here. That's how I got my Arabian which is the best horse I encountered in my playthrough so far. (There's possibly higher/better quality horses out there)
The horse’s Speed represents the fastest it can go. Racing horses often have higher points in this stat while common or work horses have the lowest.
Acceleration is how fast the horse can go into full speed. Be careful when riding a horse with Acceleration points in crowded areas since it’s very possible that you’ll run over someone or bump into things if you don’t control your speed.
Handling determines how easily you can steer or control the horse. Elite level handling is the best quality for this stat while heavy is the lowest quality. Heavy handling is usually a part of larger, sturdier horses like the Shire or Hungarian Halfbreds. You can still use them in combat or normal travels but don’t expect them to be as responsive.
Physique represents your horse’s overall build. Some aspects are fixed such as breed, gender, and coat. The only aspect affected by this is the weight, which will be affected by what you feed and how you regularly feed your horse.
Stamina determines a horse’s overall endurance. Higher stamina allows it to gallop longer and maintain that speed, particularly useful for escaping the law or chasing a target.
Health determines how much damage your horse can take, though some damage sources like high falls or train collisions ignore this stat as they can instantly kill your horse.