I'm in Thailand at the moment, enjoying all the fabulous food and ordering from street stalls whenever the stall looks popular. I've been watching the cooking whenever I can. I've seen something added to Thai iced tea that I believe is a thickening agent.
Here's what happens - the vendor adds some tea leaves to a tea sock in a metal container, adds hot water and steeps it briefly. The sock is removed and the tea poured into a big plastic cup. Two powders are then added. One is clearly white sugar, the other powder is also stark white, very finely powdered, and not caked up at all, despite the tropical heat and humidity. These are swirled around with the hot tea briefly, to dissolve, and then the liquid is poured over a big glass or paper cup of ice. After that the condensed milk goes in.
I've seen agar-agar sold in the markets here, but I don't know for sure that that's what the second powder is. I can pretty much rule out powdered milk since it's not truly white and would likely cake up in the humidity. I can't rule out coffee mate or any number of other substances. Though the coffeemate would likely be kept in its original packaging. The powder I'm seeing has been removed from whatever packaging it was originally in and put in a glass jar. This sort of supports my theory that it's agar-agar, since that is sold in plastic bags that would spill the stuff all over if it were being used by a street vendor.
My Thai is nowhere near good enough to tackle asking about this ingredient. Nor would I expect the vendor's English to be up to translating that one. I've no objections to the thickener, by the way. In fact I like it and would like to know how to reproduce it at home.