Inspired by the tree fort cocktail ask, is there a cocktail that changes a lot as you drink it?
Any cocktail will change over time, but there are some where that's intended and some where it's not.
Shaken cocktails like a Whiskey Sour are generally intended to be consumed quickly—you typically shake a cocktail that involves fruit juice and other sweeteners to get a lot of microscopic bubbles suspended in the relatively thick liquid, but after a time those bubbles go flat. What's more, the human tongue tastes sweetness way worse at cold temperatures, so since shaken drinks are balanced to taste good immediately after being chilled, they'll end up far too sweet if you let them come to room temperature.
Stirred drinks like a Manhattan go the other way: they don't have juices or syrups so they're higher in alcohol content by volume, and as a consequence often have flavors that are closer to acquired tastes (alcohol burn, bitterness, savoriness). Because they're more intense you often want to drink them slowly, and because they're less sweet they're more amenable to being consumed at room temperature. They'll still taste different at room temperature because of how your tongue works, but they're good in different ways rather than just being bad.
At the far end of this are cocktails served over ice (ideally one large cube), such as a Negroni. Instead of getting warmer, these slowly get more watered over time. They often start very strong, so even fairly watered they've still got plenty of flavor going on, but the intention is that they last a long time and get less intense across that span.