Depends on the drink you are drinking, but most drinks are designed to taste their best when cold. Usually, if a drink isn't cold it tends to be acidic, overly sweet, or overly bitter because it has to be over flavoured to taste right when cold. Essentially, cold mutes flavours and can make flavours change slightly.
For example, when a coke is warm it is super sweet (and a little over acidic), but when the coke is cold it is considered refreshing. Another example is beer or black tea usually tastes super bitter when room temp, but cold generally smooths out the bitterness to make it palatable. Also, carbonation stays suspended better in colder liquids so that can change how your tongue interprets the flavour a little bit.