No problem.
All the full-service restaurants had unsweetened tea.
Also, I recall a kiosk for tea in Epcot (outside China) and another inside Animal Kingdom (in Asia, I think) that had multiple unsweetened tea choices. As for Magic Kingdom & Hollywood Studios, I can't say I had the opportunity to locate an iced tea.....the Margarita from Prime Time was fantasmic......oh, Prime Time has to-go cups, they have unsweetened tea.....