Cold sensitivity. It could be due to root sensitivity, sometimes secondary to gum recession, or root erosion. It could also be due to a broken or decayed tooth or some dentistry that is is need of replacement. Sometimes new dentistry may be cold sensitive for a period of time, but you should notice a trend towards less sensitivity. You should visit your dentist for a thorough examination.
Sensitivity. You probably just have sensitive teeth. Tooth sensitivity occurs when dentin, the underlying layer of your teeth, is exposed. Dentin is porous and allows hot, cold, sweet, and acidic substances to enter and stimulate the nerves and cells inside your tooth, resulting in discomfort. Tooth sensitivity is extremely common, use a desensitizing toothpaste like sensodyne to offset any discomfort.
Cervical Sensitivity. Cervical (gum line) sensitivity often occurs when the gums are receded and a more sensitive portion of the tooth is exposed. I would suggest a sensitive teeth toothpaste. (sensodyne, colgate or crest for sensitive teeth).