Acting Governor Abdul Rahman Kabiri told the AP news agency that at least 30 people were killed and that rescuers were using their bare hands and shovels to try to reach survivors on Wednesday.
Emergency officials could not immediately be reached to confirm the toll, which is expected to rise.
Large swathes of Afghanistan have been covered in snow over the past 24 hours as a major storm has interrupted a mild and dry winter.
Avalanches are common in Afghanistan's mountainous north.