Had the same thing happen in a Mooney 201.
IO360 engine,  Air filter iced over and I had the ram air open.
The mixture control sensor is just behind the ram air inlet And it iced up.
the mixture contreol said "I have no air, I don't need any fuel". Engine
stopped!!
Needless to say once I closed the ram air the engine heat melted the sensor
ice and the engine started again.
Incidentally, any of you Mooney drivers should know that a Mooney engineer
told me "Don't use the ram air on a fuel injected engine".

Hank Huddleston