Most toothpastes will clear away bacteria growth and acids from food and drinks. Toothpastes with the American Dental Association (ADA) Seal of Acceptance always have fluoride, which strengthens and protects teeth. If you want a non-fluoride option, stores carry toothpastes and powders made with natural ingredients that don't have ADA testing and approval.
If cold or hot food or drinks make you cringe, pick a toothpaste for sensitive teeth and let your dentist know.