My MIL, wife, and I all recall seeing illustrations of a garment called a ‘pudding’ which was like a big inner tube around a child’s middle, worn to protect him from falls while learning to walk. But when I search, all I get is the pudding hat, which has the same purpose:
Was the garment we recall ever a thing? Are we the victims of a Mandela affect? Or have we all been subject to the same bad history?
This article shows the waist version:
Okay, now that the question has been factually answered, may I just say what a lovely thread title? I’ve been drinking.
Thank you, that’s just what we remembered. That article doesn’t talk about it much, and is generally terrible though. I wonder it we can find a better source?
*bows*
I read about this kind of “pudding” in the book If You Lived in Colonial Times, by Ann McGovern.
Do you really recall somebody wearing that? How old are you? 
The “puddings” I am vaguely familiar with are nautical ones used to protect a mast where it is crossed by a yard, or more generally any sort of soft fender. They can be covered with spun yarn, for example.
I thought this was going to be about the theory that the phrase “I’ll eat my hat” refers to a type of meat pie called a hatte.
It is entirely possible that is exactly where we are are remembering it from.