From the original story, we do catch a glimpse of Jack's dad -- and the glimpse in uncompromisingly horrific. I think this is why the element of sensitivity which Gyllenhaal injected into the Jack Twist character was very apt, as Jack would have attempted to be the exact opposite of his unloving, stern father (if you believe in certain aspects propounded in mainstream psychology). The polar opposite would have been Jack's mother, and her portrayal in the movie is in keeping with Gyllenhaal's projected sensitivity.
The scene in the original story which I will forever associate with Jack's father is the horrific urination scene close to the end of the story. Mercifully, the film did NOT choose to include this scene. But this particular part of the story demonstrates the brutality of Jack's father -- certainly hinted at in Ang Lee's screen adaptation.
For those unfamiliar with the short story, I excerpt the passage from the online-version. It is the monstrum horrendum of the section dealing with Ennis' visit to Jack's parents.
He stood up, said, you bet he'd like to see Jack's room, recalled one of Jack's stories about this old man. Jack was dick-clipped and the old man was not; it bothered the son who had discovered the anatomical disconformity during a hard scene. He had been about three or four, he said, always late getting to the toilet, struggling with buttons, the seat, the height of the thing and often as not left the surroundings sprinkled down. The old man blew up about it and this one time worked into a crazy rage. "Christ, he licked the stuffin out a me, knocked me down on the bathroom floor, whipped me with his belt. I thought he was killin me. Then he says, 'You want a know what it's like with piss all over the place? I'll learn you,' and he pulls it out and lets go all over me, soaked me, then he throws a towel at me and makes me mop up the floor, take my clothes off and warsh them in the bathtub, warsh out the towel, I'm bawlin and blubberin. But while he was hosin me down I seen he had some extra material that I was missin. I seen they'd cut me different like you'd crop a ear or scorch a brand. No way to get it right with him after that."
Horrible!