As I probably knew once upon a time, the Muppet I identified as a "Cookie Monster prototype" in this video has a name. He's the Beautiful Day Monster, seen above with the late Mr. Hooper. The Beautiful Day Monster is called The Beautiful Day Monster because in one Muppet routine, he ruined a little girl's beautiful day.
He appeared in all sorts of sketches they did, including many on Sesame Street under different names. Sometimes, they reconfigured his appearance a little with add-ons or maybe interchangeable parts. It's kind of like the way the Law and Order TV show used to use Danny Burstein.
Darren Foulds wrote in to note that The B.D.M. in the "Windy" video is, as I certainly recognized, "voiced by Frank Oz, the same as classic Cookie. Beautiful Day and Cookie were designed and built together for a snack food commercial in 1966 that never aired. The Muppet who became Cookie Monster became one of the more famous Muppets while Beautiful Day Monster never quite reached the same level of fame."
I guess it's similar to being one of those cast members on Saturday Night Live who never got a movie deal. Poor Beautiful Day Monster.