When two nations collide, more than just pure military power (or in the case of Pathfinder and similar RPGs, military and magical power) determines the outcome.
You're right... if a nation has a land that is inhospitable to invaders, has sufficient military might to slow them down, and has notably superior magical power, then if they act in a coordinated fashion they are very likely to win.
Making matters worse is that the Land of the Linnorm Kings (LotLK) is just a group of smaller kingdoms, each with their own leaders, military units, internal problems, interests, and so on. Their culture focuses on individual accomplishment and not necessarily toward unity except as a matter of pride to belong to the Ulfen people.
So you're putting together an idea for a disparate group of leaders of separate kingdoms who don't see eye to eye and have their own problems to deal with, to come together in order to drive a superior force from lands that were forcibly taken in only a month's time ages ago, a superior force that has just had its supernatural immortal ruler returned (i.e. Reign of Winter has happened in your world).
You'll need to come up with a couple of things. First you will need to find a reason for the Linnorm Kings to work together. The land they will reclaim will be sizeable but who will get it? Why is it valuable? Pride? Consider a confluence of events that make taking Irrisen back, and more particularly taking it back within a specific timeframe, important. Possibly The Great Linnorm will appear in Irrisen and whomever defeats this legendary fey dragon will be proclaimed High Linnorm King. Perhaps an artifact weapon of some kind has turned up and Baba Yaga is either prevented from finding or obtaining it or has no interest in it, but will resist anyone else's claim on it. The point being that the Linnorm Kings have gone this long without trying to unite the Ulfenfolk and take back Irrisen, so what has changed to make them willing to work together to do it now?
Second you will need to find a reason to reduce Irrisen's efficacy. Historically Irrisen has been well enough organized that Baba Yaga has been able to maintain control over a lineage of powerful spellcasters and a huge population of monsters. They've not shown any indication that Irrisen is in any way weakening, events in Reign of Winter notwithstanding. Perhaps The Great Linnorm draws power from nearby magical sources, essentially weakening spellcasting or at least limiting, say, divination and/or teleportation magics cast in the region. Or perhaps the artifact grade weapon has a similar suppressive effect. This would stymie one or two key magic-driven advantages of Irrisen forces, namely intelligence and mobility.
To reduce the potency of the monster based army, you could either have a similar aura as the magic suppression but this instead increases hostility and rage. The skalds of the Ulfen could bend this to enhance the rage of their warriors while the monsters might go over the edge and start fighting amongst themselves. Or perhaps some over-achieving orc leader from the Hold of Belkzen has found passages below the Kodar Mountains directly to Irrisen and is recruiting her monsters away, promising wealth and riches (or fresh meat) for any who join them in fighting the defenders of Lastwall, an area which is less demanding physically than Irrisen and defenders who might be considered easier prey (at least when being pitched by a particularly glib orc diplomat).
Note that thus far I've only mentioned things which would have happened completely outside the efforts of the Linnorm Kings. They would simply be trying to take advantage of an opportunity. Extra points if you drum up a scenario where one or more of the Linnorm Kings have actually acted to cause one or more of these events, especially if it was a slow play and *particularly* if you can weave in the effects of Reign of Winter to reflect that this person or group of people were working behind the scenes for years and it was almost ruined due to RoW and now they are finally getting to bring it to conclusion.
I'm not sure where you plan to take this, to have Irrisen fall and the LotLK grow back to its original size or to have Irrisen hold off the invasion, or somewhere in between. Also consider what other groups in the region might due in all of this. Would there be interest from Belkzen if humans were invading a stronghold of monsters and winning? Would the Mammoth Kings be concerned that Ulfen warriors are now essentially just next door and have assumed control over a large portion of land? How will the Linnorm Kings hold their new (old) winnings? Will they consider inviting settlers from other regions? Other races? Might they strike peace with a group or species who is typically considered "evil" but is willing to stick to the laws of the Linnorm Kings in exchange for ruthlessly driving out the other monsters?
Just food for thought. Good luck. It sounds interesting and I hope your group enjoys exploring the possibilities. :)