Yes, horses can sprint indefinitely without consuming stamina. That said, stamina is still valuable for two other reasons: It protects you from being dismounted when attacked, and if you rapidly press the sprint key you will get big boosts of speed on your mount (but at a much higher stamina cost). Of note, only horse mounts have the endless sprint trait. Other upcoming mount types will have different special traits.
Currently my friends and I have 2 horses. For pve we level our stead to increase his carrying capacity and for pvp we level a horse for speed as if you hold down the sprint key on a mount you'll have unlimited sprint... its a bug that has been around since alpha.
So what's the point in horse stamina if it still gallops even after the stamina runs out?
We've already explained it to death. You'll just have to go test out what we said in-game if you aren't grasping the full concept yet.
I went with an even split between speed and stamina with a Gaited Horse. This is because speed boost buffs applied to your character apply while mounted and since the true speed comes from Sprint not Gallop (note: you can also use potions while mounted, noteably speed potions). I use Rapid Maneuver, mount, use a Speed potion, then I just spam the Sprint key. Fastest way to travel hands down. I blow past pure speed horses even without the potion or Rapid just because I'm actually at a higher speed for longer.
Suffice it to say there's multiple ways to buff your speed on your mount, but the only way to buff your Stamina is to feed it. Pretty nifty to be able to take punishment and keep on riding by too.