Well, well, well. Seek and ye shall find. Yesterday I wondered if other full opening ceremonies were online. I then found a bunch of them listed under 'Olympic Ceremony Database'. Obviously, I haven't had a chance to look through all of them yet, but the more recent ones are complete.
Included is some footage from the very first modern Olympics, Athens 1896. There is less than a minute of footage. It looks verrrry 1896. My guess is that the old ones are all just small clips.
Internet, you have delivered again!