The story was written in an omniscient point of view with beginning and ending lines in first person. I'm unclear who the narrator of the story is. It is about 14 pages long and includes some nice details and layers to the story. For example, some neighbors' views of Mrs. McNair riding her horse recklessly and her husband's television productions and the so-called magic of transmitting images of people across space and time. Godwin did a pretty good job of creating a palpably mysterious atmosphere and state of mind of Mrs. McNair. And, Blue Boy and the horse also suggest the alternate realm as well with their behaviors.
As the young woman was never given a first name, she seemed ghostlike as well. The romantic small town in which the young woman and her television producer husband lives and the main character rides her horse is watched by the local farmers and their wives and is judged to need to have a child.
There is also an interesting exchange between Theodore Dreiser and John Cowper Powys about ghosts. Evidently, Powys was quite a character; he wrote novels and believed in ghosts.
"Dream Children" was published in Godwin's collection of the same name in 1976 and included in Tom Jenks's and Raymond Carver's American Short Story Masterpieces.
Godwin's web page
New York Times Books page
Library of Congress page
E Notes web page