Oh hey, that totally sounded familiar :) Pretty sure this is from Konyok Gorbunok (The Little Humpbacked Horse), a 1975 Soviet cartoon based on a famous Russian fairy tale. The bit you're describing is at 1:07:30 of https://youtu.be/fKc22eSL1gA.

This doesn't quite fit several of the points you remember (very much in line with the post!), so perhaps it was some other edition of that same story.

EDIT: so, I just plugged your description into ChatGPT and it gave the exact same answer, including an identical timestamp! Weird.