Common sense doesn't work here.  The temperature that's important is at the cylinder walls.  That temperature is governed by the thermostat.  Doesn't matter what the "outside" temperature is.  Thermodynamically the outside temperature is the cylinder wall temp.

Don't mistake performance for efficiency.  Cold air is more dense so more air can pack into the cylinder chamber.  Fine.  It's still colder than summer air and the energy to warm it has to come from the compression stroke.  That means the temperature at ignition is lower.  Since it is denser there can be more fuel injected and an overall higher power output.  That does not imply the efficiency is greater because it takes more fuel to get that additional power.  It's more complicated than it seems.