I am not familiar with your machine,but it has a carb. Snow throwers dont have air cleaners. But they do have an airbox that traps some exhaust heat so the carb wont ice up. Find the muffler and aft of it will be a metal box. Underneath you find a carb.

In your situation I would run some Gum-Out or similar in the gas tank, for at least an hour of operation, preferably two hours. You don't want to run this stuff all the time, because it might degrade rubber or plastic seals somewhere in the fuel system. But you can run it for a few hours, and see if that solves your problem.

Gas: I agree with Eric completely , since your not involved routinely in Small Engine Repairs go with a Fuel Treatment Top End Lubricant form of Carb Cleaner . Lucas has a Great Product in 6 Oz Bottle which both cleans and lubricates (Gasket and O-Ring ) Safe. Also numerous other Manufacturers have similar Products . Just see your Local Supply Store . If this does not clear up you problem then a hands on Carb Inspection and Internal Cleaning will be needed , 1st try what Eric has advised , you may not need anything further . Perhaps CG or Tomplum can assist you further with their expert opinion , sounds like one of the internal carb fuel circuits is fouled , but they will fast path your troubleshooting..Ty !

I always use Lucas Fuel treatment with Satabil. Also regarding the surging problem you have. I have the same machine but the bigger model. I had the same problem and it turned out it was the plug. I changed it (to an E3) and the problem went away 90%. Per Ariens tech support, a little bit of surging with no load is normal with the Tecumseh Snow King . The reason being that the engine is designed and tuned to run under heavy load.

Zoulas : I agree with the E3 Plug accolades ! This new Plug Technology has been Debated on another Thread within the Forum , I believe in the Merits of it Design Spec's . I have just finished the R& R of my Newly acquired Lawnmower from last fall , and low and behold when I pulled the plug to inspect it , it was a E3 lol. The mower is approx 2 yrs old with a new generation B&S Engine . I have no idea if the Plug is OEM , but the mower has operated Great in my 2 acre former farm acreage (lots of mixed dense grass). I guess time will tell of its merits over previous plug design. As for the Tec. Engines I hear that they are engineered as a rather lean burning unit , which as you have indicated may result in the hunting (surging) when not under load. I await Cg or Tom to validate !

Our Ariens 624 snowblower, two years old, has a 6 hp engine, overhead valve type. From day one, the first time it was started, it has had uneven idle. Not as severe as described by the OP, but not exactly smooth, either. I suspect that the carb is designed and set up to comply with EPA regulations regarding air pollution. Since the engine starts easily and reliably when cold(using the primer button) and it also performs well under load, I ignore the uneven idle. When its time for a tune-up, I will try an E3 plug.

I have an Ariens 7524 with a Tecumseh Snow King. It also has an uneven idle when not under load. When under load it runs great. It's been like that since day one. It doesn't bother me since I've seen people post about this before.

On the plus side it starts very easily when cold and IMO seems good on gas. :)