Gazbag, I really, really like your Ice token mechanic, and I think you succeeded in implementing it in simple yet compelling cards. Design-wise, I like them all; they mostly require some balancing. And they look great!
I'm not decided whether I prefer Ice tokens to be removed each turn or after shuffling, so I'm going to evaluate your cards with the mechanic as-is, for now. My general stance is that few Ice tokens on gained cards will rarely make a considerable difference so I'll often advocate more tokens.
Snow Hag: I don't think the similarity to Witch is a problem, as many official cards are redundant as well. But the Curse needs to come with at least 4 Ice tokens so it's guaranteed to miss the opponent's shuffle even if SH is played in turn 3. Otherwise it's just too strong for $4. Even then, looking at Young Witch, SH would probably require an additional nerf to justify the cheap cost.
She doesn't look like a hag at all but in case you named her this way to account for Asper's and my fan card Snow Witch, that's appreciated
Yeti: Ice tokens seem like the perfect solution to make a vicious trashing attack acceptable. I suggest you make Yeti a pure freezing attack (using Pacovf's terminology) to make the card more reliable and because you already have a curser in the set.
Venturer: Good idea in general but in it's current form I find Venturer too polarized (it's only good with strong trashing) so I would raise the cost and only make it give one or two Coppers. Also removing Ice tokens from other cards, with regards to some other Ice token cards as well as negative self-synergy, doesn't really seem like an upside on Venturer. That on top of an on-gain effect similar to Frozen Cache's (which I like more), makes me inclined to say, scratch Venturer (in its current form) from the set.
Rediscover: This combination of effects absolutely has to be in the set. But I fear rediscovering Provinces might be broken. Maybe not though, as one or two Ice tokens on a card often won't matter, unless you're drawing your deck each turn. I'm curious what you find in playtesting.
Mounain Village: Delayed gaining is not a huge enough downside to a card that self-synergizes to become a card better-than-Bazaar to justify a cost of $2. The concept by itself is great, it's just a matter of finding the right cost for this card.
Ice Cave: Again, cool idea but suboptimally implemented. In this case, it's terribly weak. Compare with Sacred Grove, and Ice Cave's benefit is even more marginal, so you can easily make it give +$3. Putting more Ice tokens on the Victory cards would be more interesting. Consider even 3 Ice tokens per card bought per Ice Cave in play, since you won't usually play more than two per turn.
Glacier: This looks ridiculous compared to Harem, but Harem sucks so who cares. It's a good concept but I would like it even more if it gave VP instead of coin tokens. That would incentivize you to green earlier than you normally would which is generally a good premise for strategically challenging cards. (The coin tokens incentivize it too but they make it much easier to continue greening in the late game which makes it too automatic in my opinion.)
Frozen Cache: The idea is cute so I don't care if it's actually weak or redundant. If it seems too weak and nobody buys it, try it at $5. That should be more appropriate.
The color pattern makes it look more like a Reserve.
Frost Spirit: I'm the minority here saying this card isn't actually that strong. My first impression was this should cost only $2! I realize it's quite good in a deck-drawing engine but it's pretty hard to build such a deck with this as the only support in the first place. How about this:
Frost Spirit, $4, Action: +2 Cards. +1 Action. Set aside a card from your hand with 4 Ice tokens on it.
This would be more akin to Secret Pasage; better at delaying junk but less flexible and synergistic with other cards.
Cold Storage: Another obvious concept that's just a matter of balancing. As usual, I think 2 Ice tokens are too few. Gaining $5-cost cards with a card cheaper than $5 is really powerful! Don't like the name in particular (perhaps something more Workshop-esque?).
Citadel: This seems like something Donald would do, just without the Ice token on it. Unlike many other commenters, I don't think you should get rid of it. But it definitely needs to come with more Ice tokens. Or consider setting it aside with an Ice token each time you discard it from play.