After you follow the Subrosian girl in the Eastern Suburbs, you reach Subrosia by a hidden portal.
Get the Boomerang
In the first screen of Subrosia, if you talk to the Subrosians, you learn that the temple fell into the East Plaza. Don't go there yet. You should get the boomerang first.
In the first screen of Subrosia, go down the stairs on the left. Follow the path past the Subrosian hot springs and go south to some stairs. You reach the Subrosia Dance Hall. Talk to the red Subrosian and agree to dance. You have to repeat after the red Subrosian. He will do a set of three moves, then you have to repeat them, then he'll do another set of three, and so on. If you dance well, he gives you the boomerang.
Get the Rod of Seasons
Go east until you reach the temple. In the entrance, the Season Spirits will speak to you, asking you to get the Rod of Seasons and then visit them in the four corner towers of this temple.
Go straight north and walk onto the altar to receive the Rod of Seasons. You can use it to change the seasons!
Get the Power of Winter
Go to the southeast tower of the temple. Inside, use the boomerang to hit the crystal switch (if you don't have the boomerang, read the how to get the boomerang). Follow the path through the tower until you reach a statue. Go up to it.
The Spirit of Winter will add the power of Winter to the Rod of Seasons. You can change the seasons by standing on a tree stump and swinging the Rod of Seasons.
Outside, the Maku Tree will speak to you. He asks you to search for an Essence in the woods to the east. There is nothing else to do here in Subrosia for now unless you want to win prizes in the Dance Hall or cut grass to collect ore chunks. Otherwise, go back to the portal to return to Holodrum.
Get the Shovel
Once you go east, you find Sokra sitting on a tree stump. He tells you to use the Rod of Seasons while standing on the stump. He also says that there are probably other entrances to Subrosia.
Do what Sokra said: stand on the tree stump and swing the Rod of Seasons. It will become winter, changing the landscape. Now you can go east from here, walking over the ice that had been water before.
Head northeast through these wintry woods. Eventually you reach an area where the seasons change. On the west side of this area is a cracked wall. Bomb it and go inside to find a treasure chest in the northeast corner that contains 30 rupees.
On the east side of this area is a house that says "Santa Welcome!!!" And to the west of that house is a tree stump. Stand on it and use the Rod of Seasons. Next, go up the stairs in the same screen as the tree stump. Go east and walk along the snow, then jump into the chimney of the house, just like Santa.
The girl inside is disappointed that you're not Santa, so she gives you a shovel and orders you to dig away the snow from in front of her house.
Get Mystery Seeds
Now that you have the shovel, go toward the southwestern corner of the woods. Turn it back into winter if you get stuck. Look for an area that has a bunch of snow piles blocking the path. It's to the east of the water that you were able to freeze and walk over to access this area. Dig the snow piles and go east.
Here you find a Mystery Seed tree. Hit the tree with your sword to collect the seeds. You can use the seeds on owl statues for advice. The one next to the tree just tells you to feed it Mystery Seeds.
Go to the Next Dungeon
Now go north. In theory you can climb the vines to turn it into winter, allowing you to access the cave blocked by water below, but there's nothing of interest in that cave.
Instead go west to find the entrance to Snake's Remains.