I did this a few times this year (just asked for a cup of ice water at a CS). Never got any "looks" or rudemess, CMs were always fine, like they did it all the time and it was no problem. It tastes like water. (I don't mind the water at WDW, drink from fountains and all, so don't ask me.)
At Casey's Corner, cashier directed me to the pickup window where the CM had a whole bunch of cups of water ready to go. That was the one place I was really aware of that. I never stood in a long line; kind of gauged the line before I got in and only stopped where there wasn't much wait. I remember doing this at one of the Sunset Market counters and Min n Bill's (? the boat) at DHS, Casey's and Pecos Bill's at MK. I usually got water with my CS meals, too, and might carry it around afterward. It was not a problem.
I travel light and am not lugging a bottle or mug around with me all day. I'm still trying to figure out how I'm going to carry the poncho next year.