Yeah, I'll point you at a sheer fifty foot wall and see how well you climb it. As for technology, I can get together a bunch of guys with rifles but does that mean I can overthrow the military, I mean we both have guns so what advantage could they possibly have. How about boiling pitch for your fumbling wall climbers, or ballistas, crossbows, silverite and horses.
Also consider this, the Avaar as a people have been in decline for a while unlike groups like the Germanic tribes and the Mongols who weren't. As a nomadic people they take the whole tribe with them as they go, this includes the young, the elderly and the womenfolk. They can't just leave them in the mountains where other tribes can get at them without the protection of their warriors so they would have to take them with them. They may be nomadic but they have to stop and make camp and search for food as they are a hunter gatherer society and so don't have any form of supply line to call upon, and whilst on foot they came fall prey to roving heavily armoured bands of unhappy chevaliers, Ash Warriors, Mabaris and embittered Dalish clans. If they bring their non-combatants with them how do you suppose they'll fair against an hostile local force looking for vengeance.
Suppose they don't just get slaughtered in the wilderness and actually make it to Val Royeux, how do you intent to take the capital? With no siege weapon or knowledge of siege craft in general and the great floor of trying to climb a sheer wall how do you intent to win out of the defenders? The Avaar don't have supplies and subsist on a hunter/gatherer lifestyle so they're going to lose supplies quickly as the local game and flora becomes scarce. They could try to raid farms and such but the Orlesian and nothing if not spiteful and uncaring of the lower class so a scorched earth retreat policy so that's won't help. You could try and send hunters further a field but that would diminish your besieging force making them vulnerable to sortie. Now face off against a foe who have vast supplies and resources to call upon from further afield and can simply counteract and experience the Avaar have in combat with a hedgerow of pikes and a rain of their own arrows.
And consider this, if a band of hunter will come under emotional distress just from a bad hunt believing their gods are displeased. In a hostile foreign land how long would it take before shamans start the whispers of dissent and whole tribes begin to dissert to return to relative safety and certainty of their mountain home in the face of death, disease, starvation, squabbling over loot and all the other unpleasantries that come with war.
And this is all a moot point as you still have to overcome your very first stumbling block. Why would the Avaar ever want to risk it all for nothing. They care not for Orlais or conquest and look down on the lowlands, they like their mountains and feel safe/strong there. The Avaars are individuals by nature, each tribe a separate entity, they would not be a single horde but rather a collection of smaller hordes and yet the Orlesians or the Fereldens would be one. To quote Robert Baratheon; "Which is the biggest number, five or one? One. One army, a real army, united behind one leader with one purpose". The Fereldens may squabble amongst themselves but they are just as proud a martially adept as the Avaar and now you've come stomping in their backyard, into their playfield. Remember these are the same Fereldens that ended a Blight in the shortest span in history and gave the Orlesians the boot; how well do you think some disorganised barbarians will do against that? As for Orlais, why attack Orlais? In Ferelden they have the excuse of originally being from the Almarri people so they have something to try and reclaim but in Orlais there is no prospect beyond loot to motivate them if you can even get the people together in one place with the blessing of the shamans to begin with.
Finally, point me to some proof that says the Avaar have better mages, versatility and well trained populace. I need more than your word, I need cite codex entries and articles. This is a people that have been written and exist in an albeit fictional but well documented universe, you need some in universe proof to show they'll win.
-D-