It all started with the Python in 1955.
There was a contest inside Colt to name the new gun, and "Python" won.
Since the Diamondback looked like a smaller Python, the Diamondback name seemed appropriate.
Colt just carried through with the snake theme on succeeding models.
While a horse theme might seem more appropriate, I don't quite see a "Clydesdale" or a "Morgan" and a "Jackass" is right out, although a "Burro" might fit a small field gun.