I'd be very happy to find a castle equipped with all these facilities. Especially the crops. Logistically speaking that castle must be a fricking nightmare to feed and it bugs me. I'm reluctantly forced to admit however the rest of you weirdoes mostly don't care about this kind of thing, but do not mistake my usual silence for complicity.
The logistics of Skyhold boggle my mind too. I think the devs went with the rule of cool and said 'magic' to explain everything. A castle in the mountains is hard to attack, sure, but just cut off the supply lines and it's screwed.
I have to wonder where our vast army is quartered too. How many soldiers do we have anyway? So many things left vague.
Hipster Eirene
was complaining about these things
before it was cool the game came out.

The simplest answer is that BioWare's devs are not historians. They are certainly not military historians. It's not their job. So they can put a massive fortress in the middle of a desert and have a big siege assault for it. They can put another massive fortress in the mountains with no food and scant communications with the outside world. They can put a huge city underground and feed it with overland grain shipments and lichens.
None of these things is plausible, either by reference to the real world or to the fantasy setting. But they operate via Rule of Cool, and Rule of Good Enough for Most Players, and that's perfectly fine. It's unfortunate, and makes the setting less tight than it ought to be, but these things are hard enough already.