I am not a big drinker. Other than beer (I work at a brewery), I don't even know what most drinks are. That is why I am looking for some type of menu to get an idea.
Carthay is addicting, you've been warned! We thought we'd pop into the lounge for a drink one night and every trip since we now pop in for a couple drinks once a trip! My favorite is the Side Car (good if you like lemon, it's different from other Side Cars I've come across) and then the B-52 for dessert (coffee and liqueur drink, highly recommended for evenings year-round but I don't know that I'd drink one on a hot afternoon). Have fun!
One of my favorite drinks when it's hot out (and 3pm means odds are good) is their Pimm's punch. It's a standard Disney drink (as in part of the menu that basically all bars have) but it's a light and refreshing one. All the suggestions skyegirl made are good as well, especially the double pear and derby!
My fav is the Tequila Daisy...and the duck wings. I know people rave about the biscuits. I think they are okay. The duck wings are a must do each trip.