As someone that has worked at a Husqvarna dealer and has had experience with sleds back in the 70's.
1. Huskies and other saws would often show up for "won't start". Would perform the drop test-- drop the saw holding onto the starter grip -- if it fell quickly would pull the muffler to inspect for scoring. Often found the piston scored, some were dry from no oil--as in straight gas, some oily as in wrong carb setting. If the saw dropped slowly with a plup-- plup--plup then often figured compression was not an issue. But a compression gauge, as Paul Harvey did told the rest of the story. 100 psi very minimum suggested is 130 or higher. If any piston cylinder damage was suspected pulling the muffler revealed the good or bad.
Often when a 2 stroke has poor sealing of the rings the compression blows by the piston and dilutes the fresh mixture so incorrect fuel mixture = no start. But often a customer stated," I changed the gas, the spark plug, and the air filter but it still won't start".
Also be aware of old stale fuel mix. Recommend not using fuel over 30 days after purchase as do most manufacturers. And shaking the fuel can before filling the fuel tank
2.Experience on JLO engines used on sleds. Large singles and the larger twins often had the most burned pistons. Often presented with "won't start" Always after pulling the head found a burned piston. The twins especially the 440 always burned the right piston, the one fartherest from the fan. They used a Walbro pumper carb. noted the carb set at an angle, and there was even a dam in the manifold to direct more fuel to the right cylinder. Needless to say I got good at replacing pistons. Later with new model sleds the engine was refined and produced as the Cuyuna engine, two more head studs, but more important was the carb manifold change. The carb now was mounted flat and changed to a float style Mikuni. No more issues, and a better running engine.
3. In the early 70's the recommend oil was a 30 weight two stroke oil mixed at 20 to 1. sometime around 73 or 74 a synthetic oil was recommended to replace the old oil and was mixed at 40 to 1. There was some oil that came out that was recommended 50 to 1. I have noticed a lot of newer equipment needs the highest JASO rated oil. Be sure to check with your dealer or operators manual for the correct spec. Old outboard oil just doesn't work in new equipment.
If nothing else I hope this gives some food for thought
Have a wonderful day