Freezing fog?

A car is warmer than an airplane wing because the cabin portion is filled with heated air and the engine compartment portion has the engine heat warming it from the inside.

I don't think that a significant amount of rhime ice would have accumulated during the short time it takes to climb 200 feet. I suspect that other factors were involved. Other people mentioned carb ice, although with the throttle wide open, I don't think that was the problem. Maybe the wings were already covered with frost prior to takeoff and as a result he was flying much closer to stall than he thought.

There are a number of things that may have happened to your friend's aircraft.

Carb icing is one, it is usual to take off with the carb de-icing off, because it tends to cause detonation in the engine, so you have the choice of icing the carb or exploding the engine.

That's not an issue with a fuel injected engine.

The other likely scenario is the formation of rime ice on the leading edges of the wings. Freezing fog comprises, as I am sure you know, tiny droplets of frozen water, these can be very sticky and right at the front of the wing there is a point, called the "stagnation point" where there is very little airflow, ice can impact and stick at that point and very quickly disturb the airflow over the wing.

The third aspect is disorientation. While it is easy to remain oriented in fog on a runway, as you pitch up, you are looking through the fog at an angle, so looking through a greater quantity of fog, and you don't have the visual reference of the runway, the fog will be slightly thicker, because it is slightly colder, not being in contact with the ground, and you can quickly lose visual reference.

All of the above are bad, a combination of all three can be deadly!

At a guess, your friends crash was due to ice building up in the engine's carburettor. This can happen quite quickly, reduces engine power, and hence he crash landed.

This can affect cars as well, and many engines actually run engine coolant though the inlet manifold to prevent this happening. Likewise some aircraft have "carb heating" to reduce the chances of this happening.

And yes I've had a car stop on me in freezing fog. Left it alone for a couple of minutes, and the engine heat defrosted things, and it started up again and drove normally. Now in an air plane, loosing the engine as you take off is more serious....

Fog is a collection of liquid water droplets or ice crystals suspended in the air at or near the Earth's surface. Fog can be considered a type of low-lying cloud, and is heavily influenced by nearby bodies of water, topography, wind conditions, and even human activities. In turn, fog has affected many human activities, such as shipping and transport, warfare, and culture.

cars seldom moving at 120 knots on icy streets.