My feet are cold no matter what.
My hands are generally the opposite.

On a cold day my feet are frozen in boots with wool socks on a bus, wool socks on a bike, wool socks in a car, and on and on.
As for the rest of me, it is generally warm as well in a car, bike, bus, in a tree, on a plane, etc...
I see no correlation between car = cold and bike = warm.