Accept the fact that you're stuck, and stop the engine. Don't gun the engine, which only digs the snowmobile in deeper.
Try one of these methods to free the machine.
Use a rope to pull it out.
If the machine is facing uphill, turn the skis to the side and pull the front end around so that it faces downhill. Then drive forward.
Tramp down the snow in front of the machine, “rock” the machine from side to side, and then drive forward.
Dig the snow away from the front-end suspension parts. Pack down the loose snow in front of the machine and on one side of the track at the rear of the machine. Lift the machine out of the hole and onto the compacted surface. Then drive forward slowly.
With newer mountain sleds, try to pack the snow on the downhill side of the snowmobile and roll it over on top of the snow.
Don't lift your machine alone. In some cases, people have had heart attacks from the strain. Get help.
When you’re moving again, you may gain traction with a slight side-to-side rocking motion.