Before this Stranger appears on the world map in Red Dead Redemption, the player needs to complete the Vincent de Santa mission: «Empty Promises» and the side mission «Poppycock». Head to El Matadero to the question mark marker to start this quest.
Talk to Zhou and Juan de la Vara, the latter will task you with finding a white stallion. Head to the area on the map marked with the image of several running horses in Escalera. They are also found in a large populated area south of Las Hermanas.
Using a lasso, catch and tame the white stallion, then head back to the men.
After five in-game days, a new marker will appear on your map — reach it and talk to the man, after which the quest will be considered completed.