Ice has always been harder to create, and more luxurious a process to use in comestibles, than fire. It could be gathered from the environment during suitable conditions, like fire, but wasn't so easily self-perpetuating and so having it available at times when it
wasn't easily available in the environment (when you probably most wished for it) required
special provision.
Dorftech, of course, could employ something like nethercap barrels (at least to store crushed ice, if not to generate it). Ice used for numbing (as per that link, in dentistry) seems more likely, though, than iced tea. Tea is
generally hot-'brewed' (though you can design infusions to work better at room-or-lower temperatures, that's not typical - "sun tea" is tea steeped for an hour in a glass of water warmed under a hot sun rather than a few minutes at near-boiling) and the leaving to cool part (as per
some brewing of alcohols) is perhaps Ok if it's not for immediate consumption, but actually
lowering the temperature with extravagant use of ice (diluting the product) is an anathema to me.
(I don't even have ice in my carbonated-drinks. I'd rather a full container of whatever it is than a partial one buffed up to the rim by blocks of solid water that hang around longer than the drink itself, leaving me with increasingly diluted dregs if I'm still thirsting enough to try to imbibe the homeopathic cola or fruit-juice. Similarly I'd rather have a splash of water in my whisky (and rarely even that! - maybe only in a whiskey) than ice. And while it might not have the ice in it (hopefully!) any beer that has to be drunk at mouth-numbing temperatures to be palatable is probably best avoided. This being a personal thing; other people have the right to be wrong about this, naturally...)
I'd say ice, as a separate thing, could be useful in Fortressing. Not (typically) to the scale of building ice-palaces in a desert, perhaps, even though that
is veery dorfy. Perhaps an auxilliary aspect food storage (along with salting) if it ever becomes more than "safe to store forever in an open food stockpile", untrameled vermin excepted. And as a medical
aid (enhances surgical procedures? Used for burns? Used to keep a drowning victim's remaining heartbeat slow to aid resuscitation? ...getting a bit 'modern', that, thpugh) a bit of ice might be useful if not actually vital.
But that's all a different thing from tea, and seems as unnecessary to me as combining your smelting industry to ensure your favourite
food and/or
drink having one or other of the
E170s additives. Staving off a particularly capricious noble by serving them their favourite mineral as a meal in lieu of their only other preference of Dodo Testicles (sic), maybe? Ok, so iced tea isn't
that bad, extravagance-wise, but it's not something I recognise in my experience, and doubt it's a 14thC-cum-proto-Industrial-Revolution thing. My opinion being my own.