My general understanding is that, weather-wise, where Americans would talk about it being “a nice day,” British people would refer to “a fine day.”
I still remember my first awareness of the latter. It came nearly fifty years ago, when I read Virginia Woolf’s To the Lighthouse. Looking at a Gutenberg edition of the novel now, I can see why I was struck by this usage. The very first line is, “‘Yes, of course, if it’s fine tomorrow,’ said Mrs. Ramsay.” The conversation continues (I have left out a lot of words about what Mrs. Ramsay’s son James, who really wants to go to the lighthouse, is thinking):
“But,” said his father, stopping in front of the drawing-room window, “it won’t be fine.”
“But it may be fine—I expect it will be fine,” said Mrs. Ramsay.
Fine!
Now, Americans would sometimes refer to a “fine day” — indeed, a classic song by Carole King and Gerry Goffin says, “One fine day, you’ll look at me/And you will know our love was meant to be.” But the difference seems to be that American “fine” and “nice” bring with them a positive association, and are used in contexts other than weather. (“Have a nice day!”) Whereas British “fine” is more purely a description of weather we might call “fair.” Here’s an OED citation from 1913: J. G. Wood Insects at Home iii. 337 “On a fine day, it is very interesting to watch the ants.”
After all these years, I just encountered for the first time an American use of this “fine.” It occurs in Erik Larson’s The Splendid and the Vile: A Saga of Churchill, Family, and Defiance During the Blitz. On p. 44 we read, “Beaverbook convened key meetings in his downstairs library or, on fine days, outside on a balcony outside his first-floor bedroom (the second floor in American parlance.”
I have categorized this under “Ventriloquism” — the phenomenon of Americans consciously or unconsciously adopting Britishisms when writing about British people or topics.
notoneoffbritishisms.com 
My perception is that us Brits aren’t really using fine in this context anymore. I can’t remember the last time I heard someone refer to a fine day here. In my social group we would say that it’s a lovely day.
Maybe other Brits are still using it?
Most recent OED citation is from 2004, The Independent on Sunday: “Forecasters predicted temperatures could rise as high as 29C in London, with the fine weather lasting until Tuesday.” Interestingly, refers mainly to temperature rather than to clear skies.
Yeh the temperature is more important than the clouds. I would much rather have warm rain than cold rain 😀
I (a Brit living near London) interpret this as meaning that the skies will remain clear until Tuesday. The cloudy weather later in the week may lead to a drop in temperature, but that isn’t explicitly stated.
“Fine weather” is something you’ll hear on BBC weather forecasts, but I tend to agree with Miriam that it sounds a little old-fashioned. It’s not something I hear that often in everyday speech.
I agree with Aidan above. “Fine” = clear skies, sunshine. No rain, not even showers. Temperature doesn’t enter into it. The forecast is making two separate statements: the temperature will rise, and there will be no rain.
This Brit is still using the term and you hear it in weather forecasts regularly. In my book, calm weather with clear skies would be described as ‘fine’, regardless of temperature or season. If the weather in London were 29C but under cloudy skies (most improbable in this climate), it would not be ‘fine’. But minus 2C and clear would be.
Growing up we often used the word fine when talking specifically about the weather. I wouldn’t say we used that word exclusively, but it was used often when describing the weather.
“The weather is fine, so let’s go….” or “They said the weather would be fine tomorrow.” or “It’s nasty now, but it will be fine later.” I lived mainly in New England and in the southeast.
But do you use it in that context now? I used to hear it being used, but can’t remember when I last heard it. I don’t watch the weather forecast often though, so maybe they still use it there.
I have always taken fine weather to imply a lack of rain and at least some blue sky. The Carole King lyric, however, suggests a good day irrespective of weather conditions.
I think ‘fine’ would be more how someone would describe it in weather forecast-associated speech. The only way I think I would use it in more informal speech would be to use the phrase, ‘it’s turned out fine’, which means the weather is unexpectedly nice (probably as small talk with someone I didn’t know well).
This immediately brought to mind for me the aria Un Bel Di from Puccini’s Madam Butterfly, which is usually translated as One Fine Day.
I’ve checked that Australian Bureau of Meterology and they seem to have moved to ‘clear’ rather than fine. Here, it’s all about the cloud cover, not the temperature, because we could have a 29c (approx 80F) day and it could be pouring with rain – that would definitely not be referred to as ‘fine’. Basically, if it’s a fine day you need to be able to open your windows and leave your house for a short walk by the garden.
This American interprets (and uses) “one fine day” to mean “at some unspecified time in the future.”
Here’s a thread that explains this sense of the idiom and includes both the King/Goffin song and Puccini’s “Un bel di.”
https://www.usingenglish.com/forum/threads/211397-Meaning-of-one-fine-day#:~:text=Posted%20by%20MikeNewYork-,%22One%20fine%20day%22%20can%20also%20be%20an%20idiom%20meaning%20%22,That's%20a%20perfect%20explanation.
“One fine day in the middle of the night,
Two dead men got up to fight,
Back to back they faced each other,
Drew their swords and shot one another.”
As a Brit I would refer to weather being fine, but not the day being fine. In the extract from “to the Lighthouse” the “it” is referring to the weather, not the day.
Back in 1992, Opus III had a acid-house-like number 5 hit with “It’s a Fine Day”. The lyrics were
“Tonight..
Fine night tonight
It’s going to be a fine night tonight
It’s a fine day,
People open windows.
They leave the houses,
Just for a short while.
It’s going to be a fine night tonight
It’s going to be a fine day tomorrow
They walk by the grass
They look at the sky
It’s going to be a fine night tonight
It’s going to be a fine day tomorrow
It’s going to be a fine night…”
Which suggests that both the “nice weather” and “good time” usage of “fine” are in use here.
As soon as the temperature went over 80 f. one of the tabloids would have a front page headline saying ‘Phew, what a scorcher’.
I think a fine day is not as hot as that.
This site is good on the weather:
A fine day describes the weather whereas a nice day describes the quality of the day, though no self-respecting Brit would ever wish anyone, “Have a nice day!” other than to mimic the faux sincerity of an American.
We Brits have lots of our own faux sincerities. It’s just they are probably a little more subtle than ‘have a nice day’. And occassionally it may be real.
I’m reminded of BBC Two, 1988 and Red Dwarf II Episode 1. Rimmer is pretending to learn Esperanto from a speak-to-learn tape.
WOMAN: “Mi esporas ke kiam vi venos la vetero estos milda.”
RIMMER: Wait a minute, I know this one, don’t tell me, don’t tell me,
don’t tell me!
LISTER: I hope when you come the weather will be clement.
WOMAN: “I hope when you come the weather will be clement.”
I knew that weather could be inclement, but this was odd to hear “clement” . Which is basically “fine” or “mild” as Google Translate has it.
70 years old and Texan, I agree with Nancy Friedman that “one fine day,” usually means “eventually” and has nothing to do with weather– it may be the day you get your comeuppance. I personally might say “it was a fine day” to mean things went well, but from time to time I use it to mean the weather looks cooperative with what we want to do (a fine day to go for a hike). Or maybe it looked like that until the bottom fell out…
The odd thing with the word “fine” in British English is that it can mean “just about acceptable” (eg. Yes, I suppose that’s fine) but can also mean “very acceptable, almost unexpectedly so” (eg. Oh, what fine manners you have!) the latter being somewhat similar to the use in “Fine Art”. So when people speak about a fine day, it can be confusing. I generally associate it with a bright, clear, dry day regardless of temperature, and often (but not always) with an element of surprise … “Oh, it’s turned out fine today!”