From Muppet Wiki

Mickey Moose appears in episode 220 of The Muppet Show. He hangs around backstage and annoys Kermit, especially when his friend Ronald Duck shows up.

Mickey speaks in a John Wayne-style twang, and even makes reference to a John Wayne film, True Grit. His name is a take on the famous Disney character, Mickey Mouse.

He appears later in episode 519 with Melissa as her Magnetic Moose.