Snowman's Big Head
From the Super Mario Wiki
The player needs to make their way around the mountain, crossing the freezing pond and avoiding getting knocked into it by the sliding slopes. Once on the mountain and at the ice bridge, the player needs to wait for the Penguin to get close enough for the player to jump onto its head. If the player steps onto the ice bridge itself, the mountain will begin blowing air, which will knock the player back down to the start and make them lose their cap. By using the Penguin to safely cross the ice bridge, the player can climb to the top of the mountain and collect the Power Star.
In the DS remake, the Penguin is slightly smaller, but it is still possible to jump and stay on the Penguin's head. If the player cannot do that, they should instead stand on the side of the Penguin (the opposite side in which the snowman blows).
Another way to collect the Star is to utilize the cannon at the beginning of the level.
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