The name of the white horse is Tír na nÓg. This is Irish for "Land of Eternal Youth".
This is the only time Irish actors Gabriel Byrne, David Kelly, Colm Meaney, and Brendan Gleeson appear together in the same film.
Several horses were used for the white horse during filming. Mostly they were specially trained stunt/trick horses, but for a few shots a purebred Irish Connemara Pony was also used.
The father explains to the boys that Murphy is the most common last name in Ireland, which is a true fact.