Root canal procedures remove the pulp from a tooth. Even when some tissue is left behind it is not living tissue. Endodontically treated teeth do not have the ability to feel cold sensitivity unless vital pulp tissue remains in an untreated root and this rarely is the case.
If your endodontically treated tooth seems to be sensitive to cold, the most likely cause is an adjacent tooth. A visit to the dentist where he performs an ice challenge will usually demonstrate which tooth is experiencing sensitivity.
That being said, teeth with endodontics still can feel pain due to the presence the periodontal ligament. If the tooth displays either periapical inflammation or infection it can be sensitive to pressure, chewing or percussion. Failing root canals can present as 'toothaches' as well. Cracks in endodontically treated teeth similarly can cause pain in the surrounding periodontal ligaments.