She Was Also Scared of Horses
While we don’t really know where her fear of water stems from, we can, however, understand where her fear of horses came from. In this case, her fear comes from an actual incident that traumatized her for many years afterward. After an unfortunate incident during the making of the movie ‘Unforgiven,’ she developed a fear of horses.

The Unforgiven – 1960. Burt Lancaster, Audrey Hepburn. Photo By Hecht-Hill-Lancaster/United Artists/Kobal/Shutterstock
What happened on that day was the horse threw her off, causing her to break her back. She was never able to ride again after that incident, understandably. I can totally get why she developed a fear. How could you not?
By the way, Unforgiven was her only western film, in which she starred opposite Burt Lancaster and Lillian Gish in the film.