Are there chord progressions in common nursery rhymes ? So there are these tunes everybody knows - Twinkle Twinkle Little Star, Happy Birthday, Yankee Doodle, Mary Had a Little Lamb, Three Blind Mice, etc.

I'm fairly new to music theory, and trying to understand some common concepts - chord progressions seem important, as well as cadences, and this "circle of fifths". Are there chord progressions in those common tunes (or other common simple and short tunes), and if so, which ones? Are there any other important concepts illustrated in those tunes?