Christopher Lloyd? He wore a black cape over a coat and a black hat.
Christopher Lloyd as Judge Doom, is the sadistic judge of Toontown District Superior Court and the primary antagonist of the film. It is eventually revealed that Doom is a Toon and is responsible for the deaths of Eddie's brother, Marvin Acme, and R. K. Maroon. Doom is killed when Eddie opens the drain on the Dip-spraying vehicle, releasing a torrent of dip that causes Doom to melt away.
The voice of Roger is performed by comedian Charles Fleischer.
EDIT: I watched my tape of Who Framed Roger Rabbit? on fast-forward and I didn't see ANY character with a yellow rain coat and/or a ten-gallon hat. The closest character fitting that description might be the head weasel who worked for Judge Doom. He wore a light pink. mobster-kinda of suit and a large hat. He was known as Smart A$s, voiced by David Lander.