Your biggest issues --
1) The Land of the Linnorm Kings is a collection of city states, and at best you're going to be first among equals rather than some sort of absolute ruler. (Especially if you don't have your own city.) The Linnorm Kings will respect the hell out of you, but they are NOT your pawns. (And they may well rebel if you get a bunch of folks killed by poor tactics.)
2) Look at the population counts in the cities (Inner Sea World Guide can help with this). 3.X guidelines for building settlements would then give you 5% of that number as NPC warriors. Like 1% might PC classes, most under 5th level. So that would give you your troop numbers. I don't remember the Lands of the Linnorm Kings having much in the way of population.
3) Irrisen has a low human population (and correspondingly tiny human army), but has the Winter Witches (possibly giving them a disproportionately high number of spellcasters) and more importantly a large monster population.
And so your human units may be going up against units of golems, frost trolls, winter wolves, frost giants, evil fey, etc.
So expect Irrisen to have a relatively small but extremely deadly army.
And even if you succeed at defeating Irriseni army, you still must face Baba Yaga and her followers, none of whom will be amused that some random upstarts trying to mess with the Queen of the Witches "icebox".
Because of the whole "Baba Yaga" thing, Irrisen is honestly better kept contained, than conquered.
So any sort of invasion would probably be better arranged around "reducing the territory Irrisen controls" (i.e. taking over some border towns whose citizens would probably prefer not to be ruled by monsters) than "taking over the entire country."