To throw a potential spanner in the works, you could have a Yuki-onna pop up during the hunt. Setting her up as an enemy to kill and as a trophy to bag is kinda boring and doesn't take full advantage of her intelligence, so set her up as a young, curious Yuki-onna who's simply interested as to what's going on.

Since she's a not an absolute idiot, she'll approach the PCs under the guise of a normal villager, in order to learn more about them. Depending on how nicely the PCs treat her, she can either be a boon to the hunt (pointing out where the biggest nastiest critter is or local hazards) or just spend her time hanging around the party as they're interesting to be with.
If they're too nice to her, she'll develop a bit of a crush on the nicest PC, which will potentially complicate things.

If the PCs try to attack her instead, she'll flee and spend the rest of the hunt making the PCs lives hell.


Another option is Juhyo or snow monsters (link). You could either have them as a swarm of medium-sized living snow monsters which ambush travellers by waiting until the victims are surrounded, or a single giant one that pretends to be a snow covered tree, hiding in plain sight among all the other snow covered trees.