In Aceh, if we want to order this drink in coffee shops we just mention Teh Dingin (Cold Tea), it will be served sweet tea mixed with ice like picture above. So no need to mention Teh Manis Dingin (cold sweet tea) because in Aceh generally all drinks are served sweet, unless we want a drink that is not sweet then must mention the word Tawar (Bland) like Teh Tawar or without sugar.
If in Aceh we call it Teh Dingin (Cold Tea), it will be different if we go to Medan. People in Medan mention this drink as Manis Dingin or commonly abbreviated as MANDI (in English it mean BATH). This term would be funny if we mentioned it in Aceh, because it is not a tea to be served but will be shown where the bathroom is.
In Batam, this drink has a unique designation that is Teh Obeng (Screwdriver Tea). The uniqueness because the word Obeng (Screwdriver) which means a tool to turn the bolt, I have not get a reference to why a screwdriver has a relationship with tea.
In Jakarta and beyond it, they named this drink with Es Teh (Ice Tea) without a word of Manis (sweetness). but if we order tea that is not cold then must mention the word sweet / tasteless like Teh Manis (Sweet Tea) or Teh Tawar (Fresh Tea).
If we go to malaysia, the name will be different. The People call it Tea O or Tea O Ice. so is the same in Singapore.
That's the diversity the name of a cup of cold tea. What about in your country?