My theory is that time, or rather the seasons and weather, are not literal in that movie, they're symbolic.
It's fall at the start because things are okay but are about to go downhill.
There's a snowstorm happening when Belle runs away from the castle, because that's the lowest part of her relationship with Beast and the deepest darkest part of winter.
Later, as they're growing closer, it's still winter, but it's sunny.
By the time of the ballroom scene, it must be warm enough outside for Belle to sit outside in the night with a sleeveless gown on like it's nothing. There is not a speck of snow on the balcony, the plants growing on it, or even the trees seen in the background beyond the balcony.
Yet when she leaves that night, we see a ton of snow again, because things are bad again.
There is less snow once Belle is home with Maurice.
And by the time of the mob marching through the forest, almost all of the snow is gone and a waterfall is gushing, making it look like they're on the cusp of spring. A rebirth is coming soon!
During the fight, it doesn't snow it rains, again a sign of spring coming.
And then after Beast is transformed, there are flowers everywhere and it looks like they're well into spring, and when they dance, the trees outside the ballroom windows are lush and green.
And yes, it makes no sense for Maurice to be out in the woods looking for Belle for months, nor for LeFou to be waiting by his house for months. It hasn't been months. Yet it has been. It's both. And neither.
There is no way to make sense of this timeline, because it's not supposed to make logical sense, IMO. It's there for thematic and atmospheric purposes. Which I personally love (despite the headaches it causes me as a fanfic writer!).
(I am not counting any other movies other than the original in this analysis. I personally don't consider the others canon, because they contradict too much, and even if you do, the creators of the original obviously didn't have them in mind when they created the original, so they don't help in figuring out the entire timeline of that movie and the total arc of the story that it shows.)
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