The Great British Weather

You would need to have a catastrophically low core temperature for your leg circulation to shut down due to cold. There are pretty big bore arteries pumping down there.

Feet, on the other hand...

And hands, on the other foot...

If your legs are not covered you will loose more heat through them, they do not have to shut down. Your body only has so much thermal energy, if you loose more due to legs being uncovered there is less to pass on to your feet.