This mission is very similar to Lethal Lava Land's "Boil the Big Bully"-mission. In "Chill with the Bully", Mario needs to reach the icy platform at outer right side of the level and face off against the Chill Bully. Jumping at the Chill Bully and shoving it into the icy water will reward Mario with a Power Star.
This mission is exclusive to the original Super Mario 64.
"In The Deep Freeze" features an Ice Block House, which is found to the left of Snowman's Land's starting area. After entering the house from the right side, Mario needs to navigate a short maze to achieve the Power Star inside it.
This mission is exclusive to the remake, Super Mario 64 DS.
In "Chief Chilly's Challenge", Luigi needs to face off against Chief Chilly. Just like the Chill Bully, Chief Chilly needs to be shoved off stage by jumping at him, but unlike with the Chill Bully, this has to be done three times.
The third time, though has Chief Chilly clinging to the battle by standing off balance, while being on the edge. Luigi needs to shove him down the edge in time by attacking again to defeat him.
Beating Chief Chilly grants the player "Wario's key", which unlocks Wario as a playable character.
Running and turning around will cause Mario to skid across the snow for a show distance.
If the player turns around, they will come across a few Spindrifts, a Moneybag and some coins, but most importantly...
...they will be able to see and visit a hut made of ice blocks and a base. The hut acts as a small maze. If the player succeeds in navigating through it, they will be able to gain a Power Star.
Pushing forward instead, will cause the player to come across a Snowman and allow them to explore the rest of the level.
A snowy area with pools of ice water is found after jumping over a small dune made of snow
Mario comes along a Spindrift. If he makes contact with this enemy, Mario will lose two points of health.
In the general area around there, a lone Chill Bully and a Red Coin can be found.
The Chill Bully can be fought to gain the Power Star of the mission "Chill with the Bully"
If the player climbs the giant Snowman instead, the snowman will exclaim, that Mario is a "snow flea" and attempt to blow him away. The player has to move in sync with the Big Penguin to avoid the Snowman's breath.
Mario collects the star on top of the giant snowman's head in the mission "Snowman's Big Head"
Luigi facing off against Chief Chilly in the mission "Chief Chilly's Challenge". Chief Chilly and his challenge are exclusive to the remake.