There was a strong hint that the Sheriffs thought that confiscation would be pursued, and vowed to stop such, even to the point of lethal force. Possibly why Sheriff Winder would not sign the letter.
Winder is shady and has aspirations of running for higher office, such as Governor. He won't do anything to potentially jeopardize his chances in future elections, or implicate himself in what may be viewed as acts of sedition.
He puts himself and his potential political future above all else - even if it means refusing to take a stance on an issue, out of fear of letting voters know what he really thinks. He's a politician, not a Sheriff.