I used to work on the North Slope at Prudhoe Bay. Got down to -60F in winter. We would receive new pickups in the fall and ALL lubes were changed to
synthetic before they were given to us. If the wheel bearings or rear diff were not changed to
synthetic, the wheels would not move after sitting all night in low temps. They even used
synthetic Auto Trans fluid.
These were a mix of Fords and Chev's and if it wasn't advisable to use synthetics, I believe they would have found out quickly.
I don't know where these tales come from, but I trust my experience, not unsubstantiated tales.
Our Cobra's sometimes have fancy transmissions or rear diff's that may change that. The best advise should come from the manufacturer.
Of course, you should always break a new engine in with dino
oil, valvoline racing is what I use. After a couple thousand miles I go with synthetic and
Amsoil is all I use.