Can sensitivity to cold automatically mean root canal?

No: There are many things that can cause a tooth to be sensitivie to cold. Some transient meaning they resolve on their own, others that respond to desensitizing toothpaste and still others that respond to a mouth guard to give relief to clenching/grinding.

No...: Sensitivity to cold can point to many possible diagnoses. These may include a cracked tooth, root surface sensitivity, a cavity, a cracked filling, a loose filling, a loose crown, or a lost filling. There may be others as well. A visit to a dentist will offer you the best chance of the best diagnosis. I recommend visiting a dentist to determine your particular problem.

Tooth sensitivity: Sensitivity to cold could be from large metal fillings, gum recession, chipped or broken fillings, bruxism, cavities, tooth fractures just to name some of the more common causes. Sensitivity to hot, especially lingering pain and\or when relieved by cold, throbbing pain and spontaneous aches are more indicative of teeth that require rct.

Maybe: Depending on the type and the duration of your sensitivity you may or may not need a rootcanal. If you had recent dental treatment and experiencing mild to moderate sensitivity to cold which is transitional and should go away within a few days or weeks. If your sensitivity is sever and it's been there for a long time than yes you most likely need a rootcanal. See a dentist for proper diagnosis.