Your goal for the first star of this course is to get to the top of the giant snowman’s head. There are two ways to get this star, though, but the one requires you to open the cannon and the Bob-Omb Buddy is located inside of the igloo. You will begin the stage right by the cannon and Red Coin star marker, with two different ways to go. Left leads to nothing important for now, so go right and follow the edge of the course. When you get to the tree in the corner, you can stand by it to find a hidden warp that brings you to a freezing pond, which is a pretty decent shortcut to where you need to go.
The water at this pond will slowly sap your health for even being in it, so try to avoid the waters if you can. A little ahead of you, some mounds of snow will be moving, as if they were on a track. Locate where the mounds of snow are coming from and head in that direction. Note that it will be four smaller mounds before the bigger one, so you will be able to time a bigger jump when needed. Once you get on the ledge behind the dispenser for the mounds of snow, follow the trail up to an icy bridge, which is where you want to do a quick stop.
There will be a large penguin here moving back and forth on the bridge, but if you step out on the bridge, the giant snowman will begin emitting a strong wind to blow you off. So, you will need to hide behind the penguin as it moves across the bridge (towards the camera), but the penguin doesn’t go straight across and will move erratically. However, when it is close to you on the right side of the bridge, you can actually jump on top of its head, where you don’t have to move at all, since the wind won’t hit you there. Whenever you get across the bridge, jump up to the snowman’s head and carefully make your way to the star.
In order to use the cannon, which is right next to you whenever you begin the course, you need to speak with the Bob-Omb Buddy, who is located in the igloo. Using the same method to get to the freezing pond as above, you will see the slope leading to the igloo to your left after using the warp (look for the coin trail). However, this slope is a little steep for Mario normally, so you need something else in order to reach it. By where the mounds of snow end, there are some Spindrifts in the water.
If you jump on the one closest to you and hold forward while in the air, you should reach the upper ledge behind the second Spindrift in the water. There are two yellow boxes here, with the right one containing a Koopa shell. Grab that and ride it up that steep slope, then enter the igloo. There’s not much to do in the igloo, but the Bob-Omb Buddy is in the back, behind some ice wall. You can either find the small entrance to him along the far wall or use the Vanish Cap. Once you unlock the cannon, exit the igloo and return to it. The rest of walkthrough is just aiming correctly to launch yourself straight to the star.