In the beginning of the Movie when the future sheriff(Cleavon Little) is running the hand-cart down the rail tracks, you can see a cable on the bottom of it where it is being pulled towards the camera, from the cart to the bottom left of the screen.
The hand rail carts they used back in the day we rather heavy, that's why slaves were forced to use them...and that is why their muscles were bulging(along with the fact they had other strenuous work). Possibly the cart was too heavy for the actors to push while singing, plus you wouldn't want them to sweat off all their make-up. Just a thought.