The thing that is puzzling is that it was running well before you hit the loose snow, after that, the thing does not run well, Correct! Two strokes like to run in the cold, but not too cold. Look at the kill switch it could have moisture in it, not enough to stop the engine but enough to weaken the spark. The increase in noise could be the muffler struck the snow and was forced back and opened the gasket at the head, the problem with this after running it would have oil blowing out front. I don't like the kill switch so I leave mine off, I think they kill the coil, and every time I have trouble it is the kill switch. If you have a headlight running off the coil this too could have water mussing things up. Water in the air filter would stop air from entering and would make it rich, you said that the choke needs to be on for a longer time so it is lean the water would have rendered it fat. Good luck Have fun, Dave
PS: If you are looking for a leak with carb cleaner just get the engine running (you don't need to be riding) and spray the cleaner around the gaskets. If you find a leak the engine will speed up or stall out (no need to do exhaust). One place that needs to be checked for leaks also is around the crank seals (under the covers) at the ends of the crank.