Beatrice's horse was used by Bea Klugh to reach the Flame. This saddled Pinto horse was used by the Others as a means of locomotion on the Island. The current status of the horse is uncertain, as it was tethered outside the Flame when the station blew up.
The horse was used by Bea to travel to the Flame station and contact Mikhail after the Others had lost communication with him. Later on during her stay, Sayid saw the saddled horse outside the Flame. From the length of the stirrups compared to the height of Mikhail, he guessed that someone besides Mikhail was present at the station. It is probable that the horse was killed in the explosion that destroyed the Flame station.