Is the eventual horse's savior a man, woman, boy or girl? I know you state 'doctor', but does the doctor care for it through and through, not giving it as a gift to a nephew/neice or anything?
I've found a few titles like
"Harry's Horse" and
"Chosen by a Horse" that fit part of your plot description, but it I doubt either book is the one you are describing, as the key differences in scenario easily eliminate them from being your elusive unknown title recalled by memory.
---------- Post added at 12:28 AM ---------- Previous post was Yesterday at 11:30 PM ----------
after an additional 15 minutes of searching, I'm still nowhere closer to effectively pinning down your title, frogza.
Perhaps this listing may help jog a memory loose:
WPL Kids' Reading Lists: Horse Stories