Thanks to everyone for the suggestions. I made a few modifications to the design:
Arctic Castle - $4
Action - Victory - Arctic
Each player reveals their hand, then gains a Snow for every 2 cards revealed that are not Snow (rounded down).
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Worth the greater of 2VP or 1VP per 3 Snow cards you have (round down).
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When you buy this, you may gain the top card from the Snow Gear pile.
The on-buy effect now gives the top card from the Snow Gear pile automatically, without the discard requirement. The pile is ordered with the cheapest card on top, then in alphabetical order. I have reworked some of the cards based on previous suggestions, and added a few.
There are now 2 Winter Vendors that are the cheapest card, making them the first to go with the on buy effect. I also modified them so the discard-for-buy effect has a $1 discount. In addition to allowing players go access the Snow Pile cards without having to buy Arctic Castle, by discarding before their turn (and likely before the player with Arctic Castle plays the terminal action) they can potentially receive fewer Snows from Arctic Castle's action.
To go with the discarding I also added a couple of draw-to-card Actions, Winter Cabin and Groundskeepers' Cabin. While these would (I believe) be relatively weak in a regular game, they synergize well with both the Winter Vendor's discard-for-buy effect and Snow's hand-emptying effect. They're not so good if you are trying to keep Snow in your deck, so I could balance things out for a player not pursuing Arctic Castle.
Here is the Snow Gear pile, in order:
Snow Gear Pile:
Winter Vendor - $1* ~~TWO COPIES~~
Action - Snow Gear
+1 Card
+1 Action
Each player (starting with you) may discard any number of Treasure cards from hand to gain a card from the Snow Gear pile worth up to $1 plus $1 per card discarded.
(This is not in the Supply.)
Daytaler - $2*
Action - Snow Gear
+1 Card
+1 Action
Reveal the top card of your deck. If it's a Snow, put it into your hand.
(This is not in the Supply.)
Elegant Muff - $2*
Treasure - Snow Gear
$1
You may put up to 2 cards from your hand onto your deck.
(This is not in the Supply.)
Snow Shoes - $2*
Treasure - Reaction - Snow Gear
$1
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When you play Snow, you may first reveal this from your hand once per Snow played for +1 Card.
(This is not in the Supply.)
Brandy - $3*
Treasure - Snow Gear
$2
+1 Buy
(This is not in the Supply.)
Snow Shovels - $3*
Action - Snow Gear
+1 Action
Do the following any number of times: discard a card from your hand; if it was a Snow, draw a card.
(This is not in the Supply.)
Winter Cabin - $3*
Action - Snow Gear
+1 Action
Draw until you have five cards in hand.
(This is not in the Supply.)
Brazier - $4*
Treasure - Snow Gear
$2
Look through your discard pile. You may return up to 2 Snow cards from your discard pile or hand to their pile.
(This is not in the Supply.)
Groundskeepers' Cabin - $3*
Action - Snow Gear
+1 Action
+$1
Draw until you have five cards in hand.
(This is not in the Supply.)
Sled - $4*
Action - Snow Gear
+1 Action
Reveal cards from your deck until revealing one that isnt Snow. Put all of those revealed cards into your hand.
(This is not in the Supply.)
Snowman - $4*
Action - Reserve - Snow Gear
+1 Card
+1 Action
Put this on your Tavern map along with up to 3 Snows from your hand.
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When another player gains a Snow during your turn, discard this from your Tavern mat along with half the Snows (rounded down) on the Tavern mat.
(This is not in the Supply.)
St. Bernard - $4*
Action - Reaction - Snow Gear
+2 Cards
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When another player plays a Snow, you may first reveal this and a Snow from your hand; if you do, play this.
(This is not in the Supply.)
Four-Poster Bed - $5*
Treasure - Night - Snow Gear
$2
If it's your Night phase, reveal and set aside a Victory card and an Action card costing less than it from your hand, and put both into your hand at end of turn (after drawing).
(This is not in the Supply.)
Golden Goose - $5*
Action - Reaction - Snow Gear
Gain a Gold.
---------------
When you gain a Snow, if it isn't your turn, you may play this from your hand.
(This is not in the Supply.)
Ice Magician's Cloak - $5*
Action - Snow Gear
For the rest of your turn when you play a Snow, get +1 Card and +1 Action instead of following its instructions.
(This is not in the Supply.)
Lead Glass Windows - $5*
Action - Duration - Snow Gear
While this is in play, when you play Snow, add 1VP to this. At the beginning of each of your turns, return 1VP from this. When you buy a Victory card, take the VP from this and discard this from play.
(This is not in the Supply.)
Snow Golem - $5*
Action - Snow Gear
Reveal cards from your deck until you reveal more non-Snow Action cards (other than Golems) than Snows. Discard the Golems and non-Action cards, then play the non-Snow Action cards in any order. Place half the Snows (rounded up) onto your deck, and discard the rest.
(This is not in the Supply.)
Snow House - $5*
Action - Snow Gear
+$5
-$1 per 5 cards in the Snow pile (rounded down).
(This is not in the Supply.)
Foxfire - $6*
Night - Duration
At the start of your next turn +1 Card.
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While this is in play, when you gain an Arctic Castle, +2VP.
(This is not in the Supply.)
Regal Cloak - $7*
Action - Treasure - Snow Gear
+2 Actions
For the rest of the turn, when you gain a Snow, +1 Villager.
$3
(This is not in the Supply.)