Small engines that are used seasonally tend to form gum deposits in the carburetor, and eventually they stop working altogether. This happens because gasoline is a mixture of different hydrocarbon solvents, and it includes a small percentage of gums and resins. In the off season, the lighter more volatile portions of the gasoline sitting in the carburetor evaporate away, and the gums are left behind. If your snowblower has a fuel valve, you can empty the carburetor of residual fuel, the last time you use the unit, in late winter. Just turn the fuel valve off, after you have finished, and let the engine run until it dies of fuel starvation. You might be able to improve the performance of your snowblower by mixing in a small amount of automotive "Gum-Out" or something similar with the fuel, and operating the unit for at least 30 minutes. If that does not work, the carburetor will have to come off, and be thoroughly cleaned up. Also, the ignition system does not last forever, and it will work better if the various parts are replaced every 10 years or so.

Does it start and run fine after sitting for 10 min? If so it probably is the carb icing wherein the intake right at carb will form ice due to the pressure drop choking off the intake air fuel mixture. A snowblower engine should have a metal or plastic shroud around the carb to direct warm air to the carb throat.
HTH,
Mike

Yes, it will start, but still has the same issues before. It does have a metal shroud at the intake of the carb, but it isn't icing since I am having these problems even when the temps are not freezing outside. I would like to take the carb off completely however one of the allen screws that holds the carb onto the engine is not accessible because of the fuel inlet. Really bad placement! I can't even get to it with a L-Shaped allen key!

It can still occur at a few degrees above freezing.
Mike

The bogging occurs less than a minute after starting. I have looked into the inlet and don't see any debris or ice forming. There is an inline fuel filter, could that be clogged? There was plenty of fuel in the bowl when I dropped it. I'm guessing I have to somehow take the carb off completely to try to clean it out. Just have to figure out what the easiest way to remove that one allen bolt.