Mike is right. It's not about weather. It's about looking forward to a change for the good, a turn-around. It's use is ironic, because that day is not likely to arrive:
One fine day, the world will know what a genius I am. It might be an Americanism.
Here's my favorite example:
https://www.youtube.com/watch?v=IJFTVKOQKQA
Some of the words might be hard to make out, so here they are:
One fine day, you'll look at me,
And you will know our love was meant to be.
One fine day, you're gonna want me for your girl.
The arms I long for will open wide,
And you'll be proud to have me
Walkin' right by your side.
One fine day
You're gonna want me for your girl.
Though I know you're the kind of boy
Who only wants to run around,
I'll keep waiting, and, someday, darling,
You'll come to me when you want to settle down.
Oh,
One fine day, we'll meet once more,
And then you'll want the love you threw away before.
One fine day, you're gonna want me for your girl
One fine day, oh,
Oooh, one fine day, you're gonna want me for your girl.
