Whether you're sieging the fortress itself or attempting to cut off it's supply lines, you have the enemy of time. As you mentioned yourself, fortresses are usually very well stocked. Traditionally and historically speaking, laying siege to a fortress is one of the hardest things a military commander is called to do. The longer it draws on, the worse the morale of the besieger. Historically speaking, there hasn't been a very successful ratio of successful sieges either. Castle sieges aren't brief, we're talking about months and months, possibly even years of attrition here depending on food stores.
If the enemy attempts to cut off the Inquisition via dedicated kill zones, then the reverse is true as well. Sieging anything in a mountain pass (let alone simply getting an army into a mountain pass) would pay havoc with the besiegers supply lines as well and there's no such thing as complete blanket of information to prevent its spread. It could be messenger pigeon, it could be secret escape tunnels. Hell, even slipping out at the dead of night.
Attacking farmlands may be the answer, but all they would have to do would be fortify some to make them unattractive targets and then the enemy would have to abandon the strategy. You can't 'sneak' in further inland because moving an army secretly is a bit of an oxymoron. You could possibly try to sneak attack with a small amount of people, but then that isn't a guarantee for success, risks exposure and since you've built your team for speed, it would be susceptible to a well timed pitch fork as well.
You're half getting it, half missing the point. The idea isn't to do all this stuff
while besieging Skyhold or whatever, it's to do it
in lieu of a formal siege. (See
literally the first sentence in my post: "Why besiege the place?") Because I totally agree: a siege is horrendously difficult, expensive, and impractical, and there are better alternatives to weaken the Inquisition. Which is, y'know, why I made the post in the first place.
The point is not to "besiege" the mountain passes, but to deny them to the Inquisition, probably via some combination of flying columns and partisan teams. There's no expectation of a total blockade this way - that would be impossible - but vastly reducing the amount of information and orders flowing to and from the seat of a continent-spanning organization is a worthy goal in itself. Even a minor disruption in communications and trade could be deadly, especially considering the marginal nature of the nascent Inquisition's organization and of the communities of the Frostback (?) Mountains, and would certainly have a disproportionate psychological effect on the Inquisition's leaders.
Getting into the nitty-gritty of responses to specific countermoves is even more pointless than my initial brainstorm, but yeah, if the Inquisition were to try to fortify outlying farms then one's operational response would have to be modified as well. It's the obvious first step toward a solution and it does make life somewhat harder for the attacker, but at the same time it disperses Inquisition force and invites defeat in detail; an attack on an outpost in overwhelming force might be an excellent opportunity to draw a large Inquisition army out of the Skyhold defenses and defeat it in detail.
But yes: the point is that the Inquisition's great
military strength, a well-defended fortress in a geographically difficult region, should
not be dealt with by a force-on-force collision or a formal siege, because both of those options fight to the Inquisition's strengths. The Inquisition's most obvious potential
military weakness is its food supply and its communications with the rest of the world, and attacking
those yields the most obvious opportunity for success.
I have zero expectation that this will actually be reflected in the game. I would be very interested, however, to learn the story reason for
why that is the case.