If the beverage is a brand name or a unique recipe title or includes a proper noun, capitalize it:

Frappuccino  (a coinage trademarked by Starbucks)

Arnold Palmer (named after a person)

Long Island iced tea (includes a place-name) 

But when the drink is a generic term, lowercase it:

cappuccino

cola

hot toddy

Sometimes drink names composed of proper nouns can be lowercased:

Manhattan or manhattan

Consult a dictionary for guidance or read our post on cocktail names.