Can IPA be used as a FSII with MoGas, particularly with a Peterson STC?
Oxygenates, which includes alcohol, are not allowed in gasoline used in aircraft even with a special type certificate, not even airplanes certified to use MoGas. MTBE is the one oxygenate that is approved.  

Gasoline sized hydrocarbons do not need freeze protection. Up to 1% anhydrous IPA (from a sealed bottle) can be used to clear an acute moisture issue, but the fuel should be consumed asap, IPA should not be a regular blend additive and certainly not be stored after adding to the tank.  

The reason alcohol is not allowed is that it creates more far more problems than it solves. Alcohol is strongly attracted to water which helps IPA absorb small amounts of free moisture from the fuel system but it will also absorb moisture from humid air. A very small amount of which (1-2% moisture to total gasoline) will cause the alcohol to separate from the hydrocarbon portion creating an aqueous layer that at low altitudes will cause erratic power surges or completely stop the engine and at higher altitudes is insufficient to prevent ice in the fuel lines.   

Meanwhile the octane rating of the remaining hydrocarbon mix will be severely degraded as alcohol containing gasoline is reliant on the alcohol as an anti-detonation additive.
Adding more alcohol to overcome the moisture issue by brute force will reduce the usable energy of the fuel. (joules per kg, alcohol has only 0.6 times the energy of petroleum per Kg) Up to 5% alcohol improves burn efficiency slightly more than it reduces specific energy, plateaus at about 10%, then the reduced energy outweighs any improved efficiency. Of course weight matters to aircraft.

If the plane is stored for a few months, the separated aqueous layer can cause substantial corrosion and schmoo in the system. I wish I had taken pictures of the tank and carburetor of the motorcycle I just rebuilt after sitting in a garage for a year to show what happens with gasohol, and on the flip side I have zero alcohol gasoline that can sit for years.


  NOTICE: Isopropyl alcohol in amounts not to exceed 1% by volume can be
  added only to aviation fuel(not automotive fuel) to prevent ice
  formation in fuel lines and tanks. Although  approved  for use  in 
  Lycoming  engines,  do  not  use  isopropyl alcohol in the aircraft
  fuel systems unless approved by the aircraft manufacturer.


Source PDF from Lycoming, which also specifies oxygenates shall be limited to 1%.