Usually, since you operate a snowmobile in a cold climate, it sounds like a fuel line freeze. If the engine turns over ok it's nothing mechanical in nature really. I would check your fuel line (or just take it the snowmobile inside your garage and warm it up for a while) and if that doesn't work, check/adjust the carburetor. Snowmobiling can be pretty rough at times so maybe a screw or gasket was knocked loose.
Also, before going too far, check for spark and compression first.