Jack's horse is named "Nutcracker," an oblique reference to his method of boarding - jumping onto the saddle from great heights.
In Bruce Campbell's book "Hail to the Chin: Further Confessions of a B Movie Actor" he says that the horse Nutcracker wasn't a very high quality animal, but was the only one production could secure since most horses in NZ at the time were being used in the Lord of the Rings films.