Thank you for your question on the snow thrower not running smoothly.
Because this is a seasonal engine and it is about ten years old it could have some carburetion problems.
Since you have changed the sparkplug and I will assume you have fresh fuel in the snow-thrower and no fuel was left in the snow-thrower over winter that you may have some carbon built up in the engine head and is causing it to sound like it is misfiring.
Check the sparkplug condition even though you have changed it to see if it is black. If it is black it may be running a little rich and is on the edge of flooding the engine.
Is there any black smoke coming out of the exhaust muffler while it is running?
If this continues you may have to either service the carburetor or remove the head on the engine and clean out the carbon.
Please let me know what you find out and we can continue to troubleshoot the problem.