My first search of the Internet seems to reveal it is just an old saying.
"My great grandfather who lived to a ripe old age of 92 was asked why he stayed so trim.
He said simply, `Lean horse for a long race.'
As a company, we also believe it pays to think Lean."
~Plastic Parts Owner/General Manager Jeff Jorgenson
She would tell stories of taking care of the horses with her brothers and sisters and she had a wealth of sayings that reached back into those childhood days. "A lean horse for a long race" she would quote to us whenever anyone started to put too much weight.
~Archbishop Theodore E. McCarrick