Final answer:
A patient with cyanotic skin diagnosed with COPD is likely to have hypoxemia, which presents as lower-than-normal blood oxygen saturation levels.
Step-by-step explanation:
Given that a patient with chronic obstructive pulmonary disease (COPD) has been observed to have cyanotic skin and is cold to the touch, it is likely that her blood oxygen saturation levels are out of the normal range. This condition, known as hypoxemia, is a lower-than-normal level of oxygen in the blood. Other signs that may accompany hypoxemia in COPD patients can include an increased heart rate, difficulty breathing, and an abnormal breathing rate, which are all vital signs that could be indicative of an exacerbation of their disease or another complication such as pneumonia.