Why afoot????

Why did they have one of the men hold onto the saddle and run? Why not just pair up the smallest men together? If a horse can handle Bud Searcy...then a horse could handle two small men. Why did they even want Seary to run anyway? I know they wanted yo be fair by taking turns...but they no he isn't in very good shape ..and they are trying to save people so they're on a bit of a time limit...so why bother???