Assuming that Ferelden and Orlais are actually able to work together? That's a tough one.
First off, Ferelden and Orlais despise each other due to the Occupation and subsequent Rebellion. Tensions remain high between the two nations even forty years after Ferelden regained independence. Only a common foe on par with the blight or Corypheus hoped to have them work together and that took a lot of effort. Not to mention that per the Exalted Council, the two kingdoms have very different designs for the Inquisition. Ferelden wants all trace of the organization disarmed and disbanded while Orlais wants to assimilate the Inquisition into it's army.
In short, if they tried to attack the Inquisition, it would have to be as separate entities.
Secondly, remember that the Inquisition remains very popular with the populaces of Ferelden and Orlais. Some love the Inquisitor for saving the world; others for ending the mage-templar war; and others because they revere the "Herald of Andraste". Not to mention all of the support which would be had from practical and humanitarian efforts which the Inquisitions forces and agents have lent to areas ravaged by the mage-templar war and the orlesian civil war.
I find it hard to believe that there wouldn't be massive public objection if Ferelden and Orlais attacked the Inquisition. Perhaps even large portions of the population would violently/nonviolently revolt in support of the Inquisition. An Arl would likely call a Landsmeet just to ensure that this "unprovoked invasion" is done with the will of Ferelden's people and not just a mad waste of men and resources. Ferelden's still recovering from the Blight, Mage-Templar War, Breach, and Corypheus' actions, they're not going to be eager for another straining conflict.
Hell, most folk in Orlais nobility would know that the current ruler owes their survival and power to the Inquisition. The honorable nobles would likely sit out such a war in protest while more opportunistic ones would help the Inquisition as a means of increasing their own power.
Third, the Inquisition's HQ is situated in a very ideal location for defense. They have a powerful and strongly enchanted fortress that only be accessed through one tough path and is impossible to mine or surround. The fort is fully garrisoned with seasoned, trained, well equipped and experienced defenders which can include templars, mages, grey wardens, tal-vashoth, rangers, rogues, and many more. All motivated and stern in their loyalty to their leader with other commanders and captains capable and able to use their abilities to their fullest.
Again, Skyhold is in the mountains which is a treacherous place to move a large army. (Just ask Hannibal) Inquisition ambush parties wouldn't have to do much to cause damage. Damage bridges, cause avalanches, kill or steal horses, pick-off guides and scouts, attack food trains and supply convoys and do everything possible to make the invader's lives miserable. It doesn't matter how many men are in either army, if those men are cold, demoralized, unattached, and starving, they'll break. When they break, they'll desert and go home or they'll turn on their officers and mutiny if not outright defect.
The Inquisition also possesses the close friendship of the Avvar in the Frostback mountains. They know the mountains better than either the Inquisition or Orlais/Ferelden. They could be called upon to assail and harry the enemy and provide food/supplies in exchange for keeping any booty that they find. Not that that's too much of a worry, Skyhold appears to be well-stocked enough to withstand many months of siege. A counterattack would also be costly and unlikely and the chance of success is minimal. It would also mean detracting attention from the Inquisition wherein lies an opportune moment.
The other forts and positions would be vulnerable, but a seasoned commander like Cullen would know that. He'd wisely withdraw troops from any non-vital positions to fortify key locations which would be harder to take. But as long as HQ and the Inquisitor/main leaders aren't captured, the war would be prolonged until aid could be garnered or Orlais/Ferelden give up and go home. By now, the Inquisition would also have list of the names of vital nobles and where they live. Use that information to send agents to "acquire" those nobles and you now have hostages to broker peace.
Fourth, the Divine herself has personal and/or political ties to the Inquisition. Enough to where Victoria could turn the Chantry on Orlais and Ferelden which in turn will turn the people against them. And since Orlais and Ferelden are the apparent aggressors of this war, Victoria can do this while minimizing accusations of bias or favoritism towards the Inquisition. This only would be enough could be enough to have Orlais and Ferelden call off the war to minimize their losses.
Fifth, the noble, economic and intrigue connections of the Inquisition cannot all have been for nothing. All of these allies and business partners have way too much to lose by letting the Inquisition get gutted. Many of these assets are from the Free Marches, Antiva, Nevarra, and as far as Tevinter, so they'd lose nothing by aiding the Inquisition. In fact, I could see Nevarra and Tevinter using their support of the Inquisition as a means of weakening Orlais to shift the balance of power in their favor.
So no. They'd lose because they're unlikely to work together; they're unlikely to have enough support and resources to carry through with the war; The Chantry may condemn them; their own people are likely to turn against them and they're fighting an enemy with a powerful home-field advantage and various other strengths which equal if not surpass Orlais/Ferelden's raw power.