Battle in the Rain/Snow

Does a battle in the snow fall under Battle in the Rain?

I would say only if snow is actually falling, and if it serves a symbolic purpose similar to what rain would. Otherwise I would just use the supertrope Empathic Environment.

I dont know, with the cold factor, I would expect snow to be a sister trope.

Rain can be cold, too. Battle in the Rain is not [[Troperithmetic "warm rain plus combat"]]; it's for when the mood of the scene is mirrored in the weather, the specific mood being the clash of characters is mirrored as the clashing of clouds, the clashing of sky & ground. The symbology doesn't require a specific temperature from the precipitation.

I agree this is not a matter of temperature; but that wouldn't work with a gentle snow. Of course that wouldn't work well with gentle rain either, but the thing is snow is often associated with calmer moods.

It depends, if its a snow scene with wire work then dancing on the snow is calm however most of the time Snow fighting is a slog and in no way gentle.

I'll repeat what I said in Finder: there's gently falling snow and then there's snowstorm.

I think the OP had taken the latter, though.