Snowmobile engines are generally two strokes except for a few new four strokes. Repair and troubleshooting is similar to any other vehicle. First you want to identify if it is a fuel or ignition problem. Remove the spark plugs and look to see if they are wet or dry. Do they both look the same or are they different? If different then one cylinder’s carb or ignition may have a problem. A wet spark plug could be many things. Take the spark plugs, dry them off with a clean rag and place them back into the plug wire. Lay the spark plugs on a metal part of the engine and spin the engine(try to start) Look at the plug gap as you spin the engine over, do they all spark descent? If some of the sparks look weak you could have an ignition problem. Hopefully the plug is fouled out and just needs to be replaced, try that first. If weak spark remains, check that the ground wire for the ignition coil or system is good. Worst case you could have a bad charging coil or bad wires shorting out somewhere.
If you have no spark the same problems could be true. Another problem could be that the coils are burned out, you can compare the resistance or ohms from one coil to the next one. If one of the readings is alot different than the same spot on the other coil, you have a bad coil. Also check that the positive wire is feeding voltage to the coils. Always check your plug wires and replace them if it has been awhile, especially if it seems to misfire alot. If the spark seems fine, then determine how many cylinders are too rich or too lean. If one cylinder appears lean (no fuel on plug) there may be an air leak between the carburetor and the cylinder, in the boot. Check the fuel hose coming from the fuel pump, it will spray fuel when spun over. If not, there is a problem in the fuel hose or the fuel pump is bad. Next remove the carb and check to see that the float is not stuck. Be careful to not bend the float, move it up and down and make sure that the fuel supply needle attached to it moves also. Next check the pilot and main jet located in the fuel bowl. The pilot is the small brass jet that can be removed with a screwdriver. The main jet is the larger brass jet which can also be removed with a straight screwdriver. Look through both jets, you should see clearly through the circle in the center of the jet. If not carefully clean them out but don’t scratch the jet up or it will cause problems. A single strand of wire pulled from a wire brush works well for cleaning out a jet. These are some of the most common problems with a snowmobile that doesn’t want to run correctly.