Your lips and fingertips turn blue from a lack of oxygen. In this case, the blood vessels in your extremities and the outermost parts of your body are clamping down in an effort to shunt the blood supply in towards your torso and the vital organs in it. Same thing happens with extreme cold.
So, because it's not lasting damage like a bruise, I would imagine as those capillaries will open right back up as soon as your body senses it's being oxygenated. They should turn back to a normal color just as soon your lips & fingertips have a blood supply, i.e. within minutes of being "rescued."