About the specialities of their UUs that the devs have hinted at:
Carolean infantry specializes in long marches.
I bet they get a combat bonus when they are far away from capital, maybe more bonus for longer and longer space between them and home.
Hakkapeliitta cavalry has a special thing when stacked with Great Generals.
If I remember correctly it was said that bonus is related to being stacked with generals?
So maybe it's a strenght bonus for the cavalry when on attack, dunno.
I'm glad that their UA 'Nobel Prize' is more peace-related, interesting to see what it is.
(I think I know the historical reasons for those Unique Unit details, the Swedish infantry did gruelling long marches when they stormed thru Europe, especially in the final of their grand campaigns against Peter the Great of Russia in early 1700s, they marched and got hammered by cossacks, guerrillas and harsh winter (kind of like Napoleon and Hitler later when invading Russia) and finally met Russians outnumbered in a final battle in Ukraine.
And during those times many generals and kings risked their lives by riding in the middle of their armies, Gustav Adolf even met his end while charging with his cavalry towards an enemy..)