<span>the pulse oximetry reading is most likely </span>secondary to decreased perfusion in the extremities.
The patient has no abnormality in breathing beside increased rate so there shouldn't be any issue in oxygen level.
When your body exposed to cold, the body will respond by constricting peripheral blood vessel. By doing so the body will prevent further heat loss because the blood is not exposed to the cold extremities. But it will reduce blood perfusion in your extremity, therefore the oxygen level might be reduced.