A dog may be eating snow due to a wide range of medical issues, such as dehydration. Cushing's disease, kidney failure, and Addison's disease may lead to the ingestion of snow. If a dog is hydrated and healthy, there is nothing to worry about; some dogs simply like the taste.
In moderation, snow does not hurt a dog. However, it is wise to keep an eye on a dog's snow intake; too high a quantity can cause an upset stomach or diarrhea. As long as the dog always has fresh water, dehydration can be eliminated as a reason for this behavior.