Just another fictional story.
Davis bought the song from Paul Rice, and took out copyright under his name. Rice may have got it from another composer, controversy here. Davis recorded the song in Chicago in 1940 and it was an immediate hit. He ran for governor in 1944.
The horse didn't show up until he ran again for governor in 1960. Davis had recorded the song twenty years earlier.

Davis sang at his 100th birthday (he first recorded in 1929 for RCA); he died age 101 in 2000.
A most unusual man!
Jimmie Davis

The story about Paul Rice and his authorship of "You Are My Sunshine" is taken from Wikipedia, but there is still controversy about whether he or Davis or someone else wrote the song. It may have been recorded by Rice before 1940, the date Davis recorded it. I haven't been able to verify this.