I asked these questions on "JUSTANSWER.com" and this is a dentist's reply:
If your teeth are in good health (no decay and no erosion of the outer enamel layer), then ice either shaved or as snowcones, shouldnt be a problem. You will experience sensitivity in areas where there is loss of enamel.
It would be better if you could visit a dentist and get your teeth checked, basically for intactness of the outer enamel layer.
A layer of enamel, protects the crowns of healthy teeth. Underneath the enamel is dentin, a part of the tooth that is weaker and more sensitive than enamel.When the dentin loses its protective covering (enamel), heat and cold or acidic or sticky foods stimulate the nerves and cells inside the tooth. This causes hypersensitivity.A desensitizing toothpaste, which contains compounds that help block transmission of sensation from the tooth surface to the nerve are very useful. But they require several applications before the sensitivity is reduced.
If desensitizing tooth paste/ desensitizing mouthwash dont work, your dentist may suggest in-office techniques. A fluoride gel, which strengthens tooth enamel and reduces the transmission of sensations, may be applied to the sensitive areas of the teeth. In cases where sensitivity is severe and persistent and cannot be treated by any other means, your dentist may recommend endodontic (root canal) treatment to eliminate the problem. This remoevs the nerves from the tooth, thereby removing any sensation.
I have been using the suggested toothpaste and within 2 weeks I did notice a difference!