Help me identify another movie from one line

This was one of the movies my mother dragged me along to see because she didn’t like going alone. I must have been around five years old, which would place it in 1960 or thereabouts.

I remember it was a long Western that did not hold my attention. The only other thing I remember is that there was a ball scene near the beginning where everyone was waltzing. A young woman (presumably the heroine) said “I love going around and around and around!” Years later, as an old woman, she reminisces by saying “I love going around and around and around!”

Any ideas?