I noticed his as well and it was pounding me so hard i had to counter it with charge. I decided to go with charging spearmen over hammer and shield to keep my initiative up. Can't wait to see if the ai will react quickly with new units.
edit: to be specific i played magnar for the first time. I was aware of the cold weakness but didnt think too much about it. Then Tarth declares war on me and starts sending three unit armies (to get their attack and initiative bonus) towards me in waves. They are sending 3 man units of cold staff wielding troops for 4 ranged cold damage - later they added the bonus damage from the magic rings to increase damage - but with the bonus damage from the magnar racial trait i only won these fights with the use of my sovereign blowing them up with flame dart. Thse tarth guys were two hitting all my melee units and it was totally freaking me out lol.
The problem was solved when i switched from hammer and shield to charging spearmen because then i had the higher initiative and move speed they only had time to get 1 shot off and i no longer had to rely on my sovereign. NICE.
I'm pretty sure what you're seeing is unintentional, and not some superb strategy by the AI. For one, Tarth doesn't get a bonus for using 3 guy units, they get a bonus for using 3 unit armies. In other words, they could have sent 9 guy companies at you, but as long as they don't put more than 3 of those in an army, they would still get their bonus (I hope that makes sense). What you are seeing there is the improper evaluation of importance on the step ladder tech (if they researched logistics and squads, they would have probably dominated you). I discussed this in more detail in my feedback thread.
As for the magi, the AI only has 1 mage design, and that uses frost staves. Worse, if you get far enough in game, all their shielded troops will be fielding Boreal blades. This is why all my elite troops end up wearing frost cloaks... and it's why Magnar often gets mowed due to their resists (it's also because the AI Magnar really likes those worthless low initiative slave troops). This is why whenever I play a new faction, I make sure to leave around varying troop designs that uses different elements (fire bow, fire mages, lightning spears, etc) with some nice traits... for them to use against me later on. It actually helps them out quite a bit.
As for your last point... spears pretty much dominates right now (armor piercing), while hammers and their negative initiative is just pretty terrible all around.
