Secret Bigfoot Path
Start at the elephant ski lift and ski down towards the deer step. Continue by staying against the left side of the wall and you will eventually see a hole in a fence. This leads to a secret passageway. There will be a yellow sign in the passageway with a picture of a yeti on it. Continue skiing and you will be well ahead of the rest of the racers.
Fox Location
At the top of Wolf Hill after the cut, keep to the left side of the screen until you reach a log cabin with a pile of wood stacked up in the air toward the sun. You will find the foxes on the level area right next to the house.
Deer Location
You will find the deer on the Deer run right after the left hand turn with the padding-wrapped tree that sits in the middle of the run. When you pass the tree, they are on the ledge next to the last house on the right-hand side (just before the sharp right turn).
Monkey Location
Go to the Lion's Peak station and instead of entering the run like usual, turn left behind the station to the lookout platform with the bell on it. You will find the monkey walking on the wall.
Bear Location
Ski down from station 8 along the unmarked trail with the ice tunnel on one side. Follow the left-hand wall until you can see the station 4 area ahead of you. Above the cave in the wall (at the top of that area), you will find the bear walking around.
Yeti Location
Ski between stations 5 and 6 and look for a bare tree and small yellow sign on the left side of station 5. This sign marks the beginning of the hardest run in the game--the Yeti run. Complete the run, pinball yourself into the blue ice cave and take the trail on the right. Keep an eye out for the Yeti's living room on the right side of the trail. Turn into his living room and you will find him walking around.
Owl Run Shortcut
Head down past and to the left of the Owl Run ski lift and towards the wire fence. Side-step the bank of snow and you will see a hole in the fence. Ski through the hole, down the hill and take a sharp right into the ice cave. When you finally exit, you will be at the bottom of the slopes and will have skipped past half of the run.