Drinking cold water together with meals may potentially slow down digestion by causing the stomach's blood vessels to constrict. Eventually, for some people, this might lead to slight temporary digestive discomfort; however, the effect may generally be minor. For most people, drinking cold water with meals is fine and does not cause any harm.Drinking cold water together with meals may potentially slow down digestion by causing the stomach's blood vessels to constrict. Eventually, for some people, this might lead to slight temporary digestive discomfort; however, the effect may generally be minor. For most people, drinking cold water with meals is fine and does not cause any harm.