While allowing your dog to have a tiny amount of green tea ice cream is unlikely to cause him irreparable harm, it’s best to avoid it altogether. Green tea ice cream contains caffeine that acts as a stimulant, affecting the nervous system and the heart. Ice cream can also be problematic for your dog as their bodies are not designed to digest milk after being weaned as puppies. Eating ice cream may cause your dog an upset stomach with symptoms like diarrhea, vomiting, constipation, or bloating.