Ethanol doesn't have any particular effect on single cylinder engines as compared to multi-cylinder engines. Too much ethanol will cause a lean condition, some carbs are jetted rich enough that it doesn't matter. The main issue with snowblowers is they sit for 90% of the year, and that's enough for the ethanol to attack the plastic and aluminum in the carb if fuel is left in it.
There is no benefit to running higher octane in these engines. Based on what I've seen with the RX-8's flex fuel sensor, the higher octane stuff seems to generally have a little higher ethanol content (not surprising, ethanol is an octane booster) than the lower octane stuff. If you can't find E0 gas where you live, put the lowest octane you can find into the engine. In the off season, drain the bowl of the carb and put some seafoam or Sta-Bil in the fuel tank.
My guess is you got a piece of grit in the main jet and when you cleaned the carb it came out.