When Gárulf was killed in battle, the horse served Éomer and his éored. When the éored encountered Aragorn's party, Éomer gave Hasufel to Aragorn in compensation for the presumed deaths of Merry and Pippin.
He rode it across much of the plains of Rohan, but the horse fled along with Arod when an old man (most likely Saruman) came to the three hunters' camping place to spy on them. After escaping, Hasufel and Arod met with Shadowfax. All three eventually returned when Gandalf summoned them, and he gave Hasufel and Arod back to their respective owners. 
Portrayal in adaptations
The Lord of the Rings film trilogy
In the film The Lord of the Rings: The Two Towers (2002), Hasufel was a chestnut color.
- The Lord of the Rings, The Two Towers, Book Three, Chapter II: "The Riders of Rohan"
- The Lord of the Rings, The Two Towers, Book Three, Chapter V: "The White Rider"
- The Lord of the Rings, The Return of the King, Book Five, Chapter II: "The Passing of the Gray Company"
- The Complete Guide to Middle-earth