I'd absolutely love to have attrition effects in difficult terrain for cultures not used to it, that would be logical and a good strategic addition, it would force you to plan your invasions much more than just gathering 1000 men and going to siege, desert/heavy snow should definitely impact morale,movement speed and food consumption.
However, before raising all this, the question I think we should ask is : do the current cultures bonuses make any sense in the first place?
To me, definitely not, they're not balanced at all:
-Aserai get trade reduction penalty and a discount on caravan costs, this is a player only bonus. The AI doesn't give a dam about that.
-Kuzaits get +10% movement speed for horsemen on the map: I don't even understand this. They don't field 100% horsemen armies, therefore, it's again a player only bonus should you choose to field a 100% horse army, it doesn't really impact anything else than steppe bandits, or maybe caravans? I dk if this applies to these. I don't know, but I find this useless.
-Vlandia is imo the only valid culture bonus atm, they get 20% more xp, it's the only one usefull (considering it works at all, not sure either)
-Sturgia and Battania bonuses are the most imbalanced imo. They should theoretically impact every one, player and AI, again they're not working atm. And even considering they do, they're pretty useless. They should definitely get something else
-Empires get 20% construction speed,repair and siege equipment, this is cool at the beginning, but past some point in the campaign, it becomes nearly useless. All cities reach all their buildings max pretty quick, so it becomes a 20% sieges engines building speed only. And again, the AI doesn't really mind that, so not that usefull anyways..
I think those bonuses should impact everyone from that culture, AI and player alike. They're kinda ok in theory, some are logical, like Sturgia being less impacted to a climate they're used to, or Battania being expert woodsmen, but they really feel like they've been thrown in the game at the last moment without much thinking behind them, and that's a bit of a shame, cause I think it's a good idea in the first place. Any civilization has always something they're better at than others.
I'd rather have as you suggested, attrition and immunity to it for those evolving in those condition all their lives, it's been something to consider throughout our own history, the examples are numerous, from the Crusades to 1812, and even till the two WW. Heck, even since Teutoburg, in fact it's as old as the history of warfare itself.
But they need to also fix every other one of those, so they're balanced, apply to everyone and bring specificity and an advantage to each faction, not just only sometimes everyone, sometimes the player, etc..
I'd rather have Battanians able to hide and ambush in forest than 20% speed in them. I'd rather have Sturgia immune to snow, and maybe something like HP bonus maybe, the dudes must be quite strong evolving all their lives in such harsh conditions. Global trade and growth bonuses for the Aserai and immunity to desert, would be better than something impacting the player only. I don't really know for the others, I can't figure something else at the top of my head, but you get the idea
I think they're kinda messy right now, and it's not only Sturgia that needs a fix regarding this imo