How fast does the skin of the airplane cool to surrounding temperatures?

Tony wrote:
You'll notice some have claimed to observe frost forming as I had
suggested it might,

Agreed. It's quite common for frost to form on glass and metal
surfaces that are exposed to a clear night sky even when the local air
temperature never drops below 35F at any time.

When theory and observations differ, it's the
theory that should change.

But in this case the observations are in good agreement with the theory
of radiant heat transfer to a clear night sky.

The effect is well known to amateur astronomers since it causes the
optics of their telescopes to cool down below the dew point and have
water condense on them even though the air temperature remains well
above the dew point. Various solutions are used such as slight heating
of the optical elements or installing tubes (dew caps) that extend well
past the end of the telescope and therefore don't allow as much heat
radiation to the cold, clear night sky.