'Horse whispering' is somewhat of a misnomer. Native Americans would sometimes tame a horse by jumping on its back and biting its ear to make it stop bucking (the pain would be worse if the rider's teeth were jerked by the horse's head). Some observers misunderstood what was happening and assumed the rider was whispering in the horse's ear to calm it.
Listed in the closing credits as 'equine technical advisor' is a man named Buck Brannaman. He's the subject of a 2011 documentary titled Buck (2011) which relates his own troubled past and how he became a 'horse whisperer'. In the Redford movie, there's a picture of Buck and his brother Smokie Brannaman in the montage of old family photos during a scene at the Booker home. It's the one with two young boys with Santa Claus; Buck is the boy on the left.
This is one of three films in which Sam Neill appears that is related to Montana. In The Hunt for Red October (1990), his character reveals his dream to see Montana and in Jurassic Park (1993) he is working in an dinosaur excavation in the state at the beginning of the film.
After A River Runs Through It (1992), this is the second film directed by Robert Redford that was set in Montana and where one of the main characters has the surname MacLean. However, this is purely coincidental, as the characters are derived from novels that were written by two different authors almost 20 years apart.