Fuel gathers dirt and moisture as it sits in the tank. If you did not drain the fuel at the end of last winter, then this could be the problem. Dirt clogs the filter, reducing airflow. Moisture in the carburetor contributes to stalling.
Make sure the choke is open when you start the snow blower. If the weather is extremely cold, then you may need to leave the choke partially open until the engine heats up. Ease it back slowly, and if it starts to sputter, wait a minute longer before trying again. Be careful that you don’t flood the carburetor, as this will cause the engine to stall.
The problem could be with the spark plug. If the plug is dirty, then it will not fire correctly. Cleaning will solve this problem. If the plug is worn, then replace it with another one. This is an easy and inexpensive repair.
If the spark plug wire is barely making contact with the plug, then the snow blower will run during the times that it makes contact, but stall when you go over a rough patch of ice or snow. Push down on the wire to ensure good contact.
Just as with vintage cars, snow blower carburetors need occasional maintenance. Check your owner’s manual for specifics on adjusting it. Wash or replace the filter when necessary.
If your machine had last season’s fuel, then check for dirt or a blockage in the fuel line, as this will cause sputtering and stalling. Clean out the line and refill the tank with fresh fuel.