Only a Cow by Arlene Hamilton, illustrated by Dean Griffiths

From chapters.ca:
Lucille isn't like the other cows on Charlie's farm. Not for her, standing around chewing her cud all day. She yearns to run in a real race, just like Thunder, Farmer Charlie's prize racehorse. Lucille's dissatisfaction with her lot in life - and her strange ambition - confuses the other cows. Even Thunder can hardly disguise his contempt when he reminds Lucille that she is "only a cow". She won't be swayed, and one day when Farmer Charlie takes them all to the fair, Lucille stumbles onto a racetrack, and lines up in the starting gate. "Only a cow" - we'll see about that!