Back to the fundamentals...
There is water vapor in the exhaust gas (hot), and there is usually some water vapor in the environmental air (cold).
As the exhaust mixes with more and more environment air, the temperature decreases, the water vapor content usually increases, and the Relative Humidity changes.
The
changes in
Relative Humidity (with respect to water) of the exhaust-environment mixture require our close attention.
Initially RH is low because the mixture is mostly exhaust with a little bit of environment air.
As more cold environment air mixes in, temperature lowers and the
RH gradually rises.
Late in the process, the
RH is lowering again because the mixture is then mostly environment air with very little water vapor content (compared to the exhaust), and even more is being added.
Somewhere in the middle of the process the RH reached a maximum value.
If it reached 100%, then the water vapor would have condensed on the abundant naturally occurring cloud condensation nuclei. Contrail!
If the RH of the mixture didn't reach 100%, no condensation, and the exhaust-environment mixture would remain invisible.
The question is this: Is the exhaust of piston aero engines cool and moist enough that water condensation can be reached in an environment as warm as -20°C? No, I don't think those engines were that efficient.
In
Calculations of Aircraft Contrail Formation Critical Temperatures there are tables for various engine types (contrail factors). I think the original Appleman contrail factor of 0.0336 g kg−1 was for piston engines. And here is the table.
So at 24,000 feet (400 hPa) , which may be typical cruise altitude for a piston engine aircraft, the environment temperature needs to be below -39°C (moist air) to -48°C air (dry air) for contrails to form.
The combustion products do contain CCN, and these do contribute to the condensation. More importantly there are ice nuclei in the exhaust products, like soot, SO2, nitrates, etc. It's on these that the condensate freezes.