Synonyms for Abstinent (same or very similar meaning)
WordNet sense 1 (a person who refrains from drinking intoxicating beverages):
abstainer, nondrinkerWordNet sense 2 (self-restraining; not indulging an appetite especially for food or drink):
abstentiousWordNet sense 3 (sparing in consumption of especially food and drink):
abstemiousFrom the ODE community, based on WordNetadd/edit