Where can I find a full stat horse?
Horse stats are never really guaranteed, outside of the unique horses in the game. Finding a horse with your preferred stats is going to be completely up to chance, and may take some time to find*.
Of the Unique horses that you can tame, the Royal White Stallion has four strength stars, three speed stars, five stamina stars. The Giant Horse has five strength and speed, but zero stamina, meaning that it cannot gallop.
Epona is the only other unique steed that can been tamed, though she can only be obtained by way of scanning the relevant amiibo. She has four strength, speed and stamina, and can be spurred.
The best horse you can find is actually the Lord of the Mountain, which has 5 in all stats, and can gallop. However, you can't register it at any stable, so it will escape when left on its own.
Other than that, you will have to go looking for your perfect horse.
*Horses found in the game will never have a full 5 stars in each stat. This reddit post explains that there are ideal combinations that you can find, but none of them have a 5 Strength, 5 Speed, and 5 Stamina combination.