Cool, Cool Mountain is in the main room of the castle, in the door on the left, below the door for Bob-omb Battlefield. The level is set on a snowy mountain, though be aware that you can fall off and die.
Slip Slidin' Away
This star is obtained by entering the chlmney near the start of the level and completing the slide without falling off. At a certain point, a row of coins points toward the wall; go along them to pass through the wall and find a shortcut to the bottom of the slide.
Once you reach the bottom of the slide, go through the door to find the star waiting outside.
Li'l Penguin Lost
On the snow-covered platform next to the chimney for the previous star, there is a blue baby penguin. Pick it up by pressing B and take it to the mother penguin at the bottom of the mountain. Getting hit by an enemy or falling far will cause you to drop the penguin, which becomes harder to pick up as it moves around.
Once you bring the baby penguin back to its mother, she will give you the star.
Big Penguin Race
Go in the same chimney as for Slip' Slidin Away. There will be a large penguin waiting; she will offer to race you. Accept, and get to the bottom of the slide before she does. Taking the shortcut mentioned above is considered cheating.
Once you beat the penguin (without using the shortcut), she will give you the star.
Frosty Slide for 8 Red Coins
Collect the eight red coins spread around the level; then, get the star.
Snowman's Lost His Head
Go up on the platform next to the chimney, then down to the left to a wooden platform. This platform has a pedestal with a ball of snow on it. Approach the ball and it will talk to you, then start rolling down the slide. Go in front of it, but do not get too far ahead of it. Slide then run to the pedestal with the snowman's head. If you do it correctly, the ball will go under the snowman's head to make a complete snowman. The snowman will then give you the star!
Wall Kicks Will Work
Activate the cannons if you have not done so already by talking to the pink Bom-omb on the platform halfway up the lift on the bottom of the mountain. Then, take the cannon and aim toward the ledge directly across. Try to catch on the tree by aiming above it. Then, run down the narrow ledge, defeating the enemies along the way by punching them. Long-jump across the gap.
Then, go to the lowest part of the platform above Mario, and either wall-kick or somersault onto it. Then, go near the high end. Run backwards a bit, then run up again and right away jump so that you somersault. You need to hit the vertical part of the wall. If you do, then just as you hit the wall, press A to do a wall kick and push the stick to the right. If done correctly, you will land on the top platform. Then, walk across the narrow ice path (carefully) and jump to get the star.