Marian is Cookie Hood's horse, who appears in Episode 4033 of Sesame Street. She had previously told Cookie Hood that taking cookies from people without asking, even if to give to others, is stealing. Marion hates cookies, and prefers broccoli.
As Cookie Hood is a take on the title character in the tale of Robin Hood, Marian is presumably named for Robin Hood's love interest, Maid Marian. The puppet was first used as a bucking bronco for the "Tale of Pecos Bill" in Elmo's World: Wild Wild West!