pedanther

Yes and no.

In the well scene, Snow White sings a song called "I'm Wishing", which the prince overhears and comes to sing a Sigmund-Rombergy sort of thing called "One Song". Neither of those seem to have lasted the distance; at least, I don't think I've heard either of them before.

"Some Day My Prince Will Come" shows up later, after Snow White is established in the dwarfs' cottage. I'd always assumed it was a hypothetical, but in context it's pretty obvious she's thinking about the prince she met earlier.

I have heard "Some Day My Prince Will Come" before -- although now that you mention it I haven't heard it recently -- but then, I'm old enough to remember the joke about Snow White's holiday photos.