Even though the Hawkeyes sucked when I was a kid, we watched the Rose Bowl, as it was the Big Ten's game againt the PAC-8. It was a game the Big Ten dominated until it didn't. Because the Hawkeyes sucked I was going to grow up and personally save the program when I got into college. My adult height soared to 5'8". I didn't quite accomplish my goal. And that's not to say I wasn't the toughest little kid on the block. I could lift more than most big kids. I could hit harder than most. And I never, until decades later, let my high school teammate who was All Big Ten know how jarring it was, or how much it hurt me, when I took him down in practice. Had he known, he wouldn't have gone down.
My early memories were of Indiana in the Rose Bowl with a running back named Isenbarger; sort of like a slow moving iceberg that stopped for nothing. I don't remember how that Rose Bowl turned out. Or if it was my first memory of a Rose Bowl. I recall Sophomore Rex Kern leading Ohio State, possibly against Southern Cal and OJ Simpson.
Now I am going to cheat, and look.
The Indiana Rose Bowl v. USC is my first memory of a bowl game: 1/1/1968.
Ohio State v. USC is my next memory of a bowl game: 1/1/1969.
I seemed to recall Purdue was playing on 1/1/1967, but can recall no details of who played for Purdue in that game.
And the Big Ten was so good at that time

no Big Ten team was allowed to play, even if it was the champion of the conference, two years straight. And the PAC-8 was at that time hard-up for wins and played whomever was 1st.