Snowmobile had troucle getting it started. once started would have trouble keeping it running. would also backfire after getting it started

carburator dirty from ethanol gas--put a cleaner like BG, amsoil quik shot or lucas to clean gum--or disasemble and rebuild if need-----use pure gasoline like outboard motors use----and dont store machine without draining tank

Sounds like the alternator is faulty!

The back fireing is common,but check the bushings in your drive clutch,when the inner goes bad,the clutch will not totally disingauge causing the sled to stall.

Typical backfire.

First thing that comes to mind is ignition timing.
It sounds almost like the timing isn't retarding when starting.

if it is backfirering sound like timing is out of spects

air adjustment

your carbs are out of tune

recoil rope routing?

timing or cam

fuel pressure regulater