Accurate oxygen measurements by oximetry require a good blood flow through the tissues. When your fingers are cold, the blood flow is reduced and poor or abnormal readings are possible.
Warming the hands by rubbing them together or with warm water helps improve blood flow. Also, oximetry does not measure the carbon dioxide in your blood. In the state of a severe breathing attack (i.e., bronchospasm such as in asthma or COPD), it is possible to have a normal oxygen level with severe carbon dioxide buildup.
This is not because oxygen reduces the drive to breathe, as is sometimes wrongly concluded. It is because working hard to breathe can cause large amounts of carbon dioxide to be produced, and the breathing muscles may become tired and weak and thus not force enough air for carbon dioxide removal. This can be a medical emergency. Usually this is accompanied by severe shortness of breath, wheezing and increased pulse rate.