02 FX470E Ran poorly in deep powder snow & very cold tem

Can anybody offer some suggestions to help me set up my 02 FX470E better for very cold weather riding and deep powder snow condition?
My 470 has stock jetting and starts very well in very cold weather, we had -15 degrees. 16+ inches of powered snow. My bike ran great for the first mile of trail. Then it started to loss power and stalling. It wouldn't carry 3rd gear and the throttle was starting to stick a little bit? When the bike finely wouldn't run any more I pulled off the seat and found the air filter area completely packed with snow. Also I had snow packed around the carb, which I cleared. I let the bike set for a few minutes. And she'd fire back up on the button! I haven’t had the bike out since. Has anybody blocked off the open area where the rear shock is. And I think making some sort of block off panel for the bottom of the frame would help keep snow out also? Any suggestions would be greatly appreciated

Thanks guys! The deep power was such a cool feeling, Get the old girl into 3rd gear and just pin It, lean way back and steer from the back tire and rear brake. The front end kind of just floated. I'm almost positive that the carb was icing! I was thinking about using ridged sheet plastic and form like a fairing around the motor back to the shock area and under the motor back to the swing arm pivot. Tie the three or four pieces to each other and the frame tubes, with tye wraps?