Final answer:
After ensuring the patient has an adequate airway, the immediate action to take in this situation is to check the carotid pulse.
Step-by-step explanation:
After ensuring the patient has an adequate airway, the immediate action to take in this situation is to check the carotid pulse. Checking the pulse will help determine if the patient has a heartbeat and is therefore in need of CPR or other life-saving measures. The fact that the patient is unresponsive, has cold skin, and has been exposed to cold temperatures raises concerns about hypothermia, but the first priority is to assess if there is a pulse before proceeding with any further actions.