Using dependency TerraBlender (fabric) - you'll find that Regions Unexplored remains unaffected by the season conditions provided by Fabric Seasons mod.

Things to note:
Everything works but the biome and leave colors.
Found no issue with winter weather for all biomes, they all snow accordingly.

Ditto to this issue in my install.

Same problem on 1.19.2. A mod (maybe resource pack, not sure) needs to be created for non vanilla biomes to work AFAIK