Deer

From Muppet Wiki

This Deer was made for Episode 221: Bob Hope of The Muppet Show and appeared in several other episodes, along with John Denver and the Muppets: A Christmas Together, the wedding sequence of The Muppets Take Manhattan, A Muppet Family Christmas, and episode 107 of The Jim Henson Hour.

Another one named Robert the Red Deer was seen in episode 124 of The Animal Show.