Blue skin - the medical term is cyanosis - can be due to a number of problems including asthma and other lung and breathing disorders. It often reflects insufficient blood in the extremities or low hemoglobin, the carrier of oxygen in red blood cells. Normally, arterial blood is bright red, thanks to the oxygen it contains. Skin color is a combination of your skin pigmentation plus the color of your blood. When oxygen levels decline, blood turns blue-red.
Another possible cause is Raynaud's disease, in which the fingers and toes blanch, and may become numb or painful and turn blue on exposure to cold. The root problem in Raynaud's is not lack of oxygen, but oversensitivity of the nerves controlling small arteries, resulting in constriction of blood flow to fingers, toes, nose and earlobes in temperatures that should not trigger this response. (Constriction of peripheral blood vessels is a normal protective response to conserve body heat in cold environments.)
Raynaud's disease is most common in women between the ages of 15 and 40 and can occur on its own or accompany (and often precede) autoimmune diseases such as lupus (SLE, systemic lupus erythematosus) and scleroderma. It can also be triggered by some medications, including the beta blockers used to treat high blood pressure, drugs for migraine that contain ergotamine, certain chemotherapy agents, and stimulants in over-the-counter cold remedies that cause blood vessels to constrict.
To find out for sure what caused your daughter's hands to turn blue, I recommend taking her to an internist for a review of her medications and a thorough workup. In addition, take a look at my recommendations for long term control and prevention of asthma. If Raynaud's disease proves to be the problem, I suggest exploring mind/body methods, especially biofeedback training, to learn how to warm the hands.
Andrew Weil, M.D.