The Outlaw

Sheriff Pat Garrett (Thomas Mitchell) welcomes his old friend Doc Holliday (Walter Huston) to Lincoln, New Mexico. Doc is looking for his stolen horse and finds it in the possession of Billy the Kid (Jack Buetel). Despite this, the two gunfighters take a liking to each other, much to Pat's disgust. This does not prevent Doc from trying to steal the horse back late that night, but Billy is waiting for him outside the barn.
After that, Billy decides to sleep in the barn, and is shot at. He overpowers his ambusher, who turns out to be curvaceous young Rio McDonald (Jane Russell), out to avenge her dead brother.
The next day, a stranger offers to shoot Pat in the back while Billy distracts the lawman. However, he is only setting the Kid up. Billy, suspicious as always, guns him down just before being shot himself. There are no witnesses, and Pat tries to arrest Billy. Pat does not understand when Doc sides with the Kid. As the pair start to leave, Pat shoots Billy, forcing Doc to shoot the gun out of his hand and kill two of Pat's men.
Doc flees with Billy to the home of Rio and her aunt, Guadalupe (Mimi Aguglia). With a posse after them, Doc rides away. Instead of killing the unconscious Kid, Rio instead nurses him back to health, a process that takes a month. By the time Doc returns, Rio has fallen in love with her patient. Doc is furious that Billy has stolen his girlfriend. After Doc's anger subsides a bit, the Kid gives him a choice: the horse or Rio. To Billy's annoyance, Doc picks the horse. Angered that both men value the animal more than her, Rio fills their canteens with sand. The two ride off without noticing.
On the trail, they find themselves being pursued by Pat and a posse. The pair surmise that Rio tipped the sheriff off. Doc kills a few men from long range, but leaves Pat unharmed.
When Doc wakes up one morning, he finds Billy gone and Pat waiting to handcuff him and take him back. Stopping at Rio's, the two men find that Billy has left Rio tied up in sight of water out of revenge. Suspecting that Billy loves Rio (even if he himself does not realize it) and will return to free her, Pat waits. Sure enough, the Kid comes back and is also captured.
On the way back to town, however, they find hostile Mescaleros all around. Pat reluctantly frees his prisoners and returns their revolvers after extracting a promise from Doc that he will give them back and make Billy do the same. They manage to elude the Indians, but Doc refuses to honor his word.
As Doc tries to leave with his horse, Billy stops him. The two men decide to duel it out, with a pleased Pat expecting Billy to lose. However, as they await the signal (the end of a cuckoo clock signalling eight o'clock), Billy realizes that Doc is a true friend, and moves his hands away from his guns. Doc tries to provoke him, inflicting minor wounds in one hand and both ears, but the Kid still will not fire. The two reconcile. Furious, Pat calls Doc out, despite not having a chance. Doc makes no attempt to shoot his friend and is himself fatally wounded. Pat is aghast.
After Doc is buried, Pat offers to give Billy their friend's revolvers. He also persuades Billy to give him his guns, saying that he can then claim that it is Billy in the grave. The Kid can leave his past behind him and have a fresh start in life. However, it is all a trick. Pat had removed the firing pins from Doc's revolvers. Fortunately for Billy, while comparing the guns, he had inadvertently switched one of Doc's for his. As a result, neither his gun nor Pat's fires. Billy pulls out a second, working gun. He handcuffs Pat, judging that the lawman will still state that Billy is dead rather than admit the Kid left him helpless. As he is riding away, Billy stops and looks back; an overjoyed Rio gets on his horse.

Question: who  is looking for his stolen horse ?
Answer: doc; doc