It's definitely a thing in many parts of the Old World too.

Most American houses where I live have mud rooms. I think you may be generalizing based on house design. New Englanders certainly do; Ranches do not. Split-Levels have a landing that are used as a mud room.

I think they are common in the midwest? Wherever it snows a lot, you'll have a mud room to change from outside to inside clothes. If you are somewhere that doesn't snow, you might not ever realize those kinds of rooms exist.