Tribute to McQueen?
There is a scene in Silverado where a hatless Costner attempts to mount his horse and gets carried a short distance clinging to the side of the saddle before getting in the saddle and singlehandedly chasing a group of fleeing bad guys before giving up the chase.
It appears to be a replica of the scene in The Magnificent Seven when a hatless Steve McQueen does the exact same thing, carried along by his horse until he got in the saddle to singlehandedly chase the Mexican bandits as they fled the village after their first battle with the Seven. IMO, the scenes are too similar to be coincidence. I'm guessing Kasdan did it as a tribute to McQueen.