In my last few worlds that I've played in, the rivers always spawn partially frozen and the banks are covered in snow. This often happens in desert biomes. Is this perhaps a conflict with Geographicraft?

Vanilla river biomes have seasonal effects completely disabled, but Geographicraft might not use the vanilla river biomes.

Additionally, it might be good to delete your biome_info.json file in the Serene Seasons config and let it regenerate to make sure that it properly updated to include rivers in the blacklist.