I want to add something to my server for a christmas theme and I thought I'd use Primal Winter however it adds biome generation. I thought maybe it'd be a good idea to make a separate pack/mod that Is Primal Winter lite or something that only adds the snow mechanics and the fog. Thanks!

You can already blacklist any number of biomes, or use nonWinterBiomes = [] and invertNonWinterBiomes = true (effectively turning it into a whitelist of no biomes). That will prevent any biome based modifications - but mind you, biome based modifications are how some of this mod works, i.e. the biome determines the temperature, and the weather (snow vs. rain).

I am not interested in making a "Lite" version of this mod.