So all of my freezing mechanics seem to be working as intended, a wet target being chilled freezes them and a chilled target made wet freezes them, a chilled target being chilled again freezes them. The one exception to this seems to be Ice Fan. If I chill a target with the 2 turn chill effect from Winter Blast or Hail Strike and then cast Ice Fan on those targets to freeze them, they still only remain chilled for 2 turns.
The reason I believe this is a bug with the chilled interactions is because if I cast Ice Fan on it's own and apply it's 1 turn chill effect to an enemy with one shard and then hit them with a second shard, they become frozen due to the stacking chill effects. But if the enemy has a chilled for 2 turns effect then even all 3 shards on one enemy will not freeze them as if the game isn't even registering the chilled effect from Ice Fan. I haven't progressed far enough in this play through to test the interactions with Global Cooling, however since it's chilled duration is 3 turns if the same bug was affecting all your other ice spells of lower chilled priority then this bug actually creates a crippling detriment to the Hydrosophist mechanics.
I tested the interactions on a fresh install with no mods so as far as I can tell this is an issue in the base game.