You need a Zugzwang's Scarf to enter this area. It is available as a loot drop from Icewing Mouse or from the Dragon Chest (the first one opened always contains a Zugzwang's Scarf and a Magic Feather, in addition to other useful items).
If you have at least 38 million points, you can now craft a new, extremely powerful Tactical weapon (even better than the Horrific Venus Mouse Trap), the Zugzwang's First Move.
First you need to buy the Zugzwang's Last Move from the trapsmith in the Seasonal Garden (if you don't have one already from Furoma).
Then smash it to get Chess Pieces
Now buy the Zugzwang's First Move Blueprints from the Seasonal Garden general store.
Craft the Zugzwang's First Move using the following recipe:
1 Magic Feather + 1 Chess Pieces + 1 Zugzwang's First Move Blueprints = 1 Zugzwang's First Move
This is how this location works: every 80 hours (3 days and 8 hours), the season will change (Spring → Summer → Fall → Winter, then back to Spring), and so will the types of mice available. Tactical traps are effective against all the mice, but mice of each season also have their special weakness.
Spring mice are especially weak to Physical traps.
Summer mice are especially weak to Tactical traps.
Fall mice are especially weak to Shadow traps.
Winter mice are especially weak to Hydro traps.
Thus, equip the right setup for the season. The MouseHunt Timer is useful for predicting the seasons.
Gouda cheese should be sufficient for attraction; however Super Brie is needed if you wish to catch the Spring Familiar or Fall Familiar mice (worth a 6% increase of the amplifier!)
Each season has a powerful "boss" mouse, that drops a key shard:
In the spring, the Vinetail drops the Spring Key Shard
In the summer, the Summer Mage drops the Summer Key Shard
In the fall, the Harvester drops the Fall Key Shard
In the winter, the Winter Mage drops the Winter Key Shard
Also when you're in the Garden, the Tower Amplifier bar appears. This increases every time you catch a mouse in the Garden, and decreases on a fail-to-attract (merely missing an attracted mouse has no effect). Leaving the garden has no effect on the percentage; you'll pick up where you left off when you return.
Once you have all four key shards, you may combine them to create the Zugzwang's Tower Key. You may then continue to the next chapter.