Chestnut was an old horse, a stot owned by Ser Arlan of Pennytree.
When Ser Arlan died, Duncan the Tall took ownership of Chestnut along with Thunder and Sweetfoot.
Chestnut died in Dorne, during the desert crossing between the Prince's Pass and Vaith.
If you want to learn more lore go to Game of Thrones Lore: Story of House Merryweather.
Game of Thrones is roughly based on the storylines of A Song of Ice and Fire, set in the fictional Seven Kingdoms of Westeros and the continent of Essos. The series chronicles the violent dynastic struggles among the realm's noble families for the Iron Throne, while other families fight for independence from it. It opens with additional threats in the icy North and Essos in the east. Dive deep in the big world of Westeros or Essos.With us, you will learn all the history and geography about all houses castles and much more.