Rehoming a Soft Coated Wheaten Terrier ("Wheaten") is a way of offering that dog a second chance to live in a loving home. The following should help you understand what rescue is all about, including our goals, procedures, and additional facts so that you can make an informed decision. Goal The Soft Coated Wheaten Terrier, an exuberant Irish farm dog, is happy, friendly, deeply devoted, and just stubborn enough to remind you he's a terrier. The unique wheaten coat is low-shedding but The Wheaten Terrier is known for their distinguished, charmingly scruffy appearance — their soft, wheaten-colored coat adds an extra touch of whimsy and requires regular grooming. HxtdJnl.