Tango was an Earth horse who lived in the 23rd century. Born on the colony planet of Elysium, Tango originally belonged to Heston Prescott, and would become Christopher Pike's horse when Heston died in 2231.
Tango was part of an effort by Heston to introduce horses to Elysium, which had no such native animals on that world. As an embryo, Tango was implanted into one of the mares that Heston brought to that world, and was born 11 months later. From the very beginning, Chris and Charlie Pike helped take care of Tango.
In 2231 there was an intense wildfire that swept across Elysium. Not only did Heston die in the fire, but so did his wife Willa McKinnies, along with many of the horses. Charlie Pike convinced the Starfleet rescue team to bring Tango on board the ship, and took both Chris and Tango back to Earth. He brought them both back to Mojave, to the home he shared with his wife, Hobelia.
Tango remained at Charlie and Hobelia's place for the rest of his life. When Chris later joined Starfleet, the couple would take care of Tango while he was away. Eventually Chris began the process of building his own home nearby, but decided to leave Tango with Charlie and Hobelia since Tango had lived nearly his entire life there. (TOS novel: Burning Dreams)
During their initial encounter with Captain Pike, the Talosians attempted to use an image of Tango to convince Pike to remain with them. Despite the illusion of Tango being very accurate, right down to the horse searching to sugar in Pike's pockets, the attempt did not work. (TOS episode: The Cage)