While it may not seem like it because the game is so much larger, but there is probably about the same amount of cutscenes in this game as the past games. The difference is they added a LOT more dialog that didn't have cutscenes.
I mean every single companion and 3 advisors have probably a dozen or more cutscenes each... So that's about 150 cutscenes just in Skyhold characters.
I wouldn't say there's a dozen scenes for each companion. I'd probably go closer to around 6 or 7. Maybe more if you romance them. Some companions (ie - Cassandra) seem to have a larger presence in cutscenes. I've noticed that Iron Bull has less cutscenes than others. Overall, a good chunk of the companion dialogue is in non-cutscene format and investigate options.
@OP: There really isn't any cutscene content outside of main quests. You might get an occasional dialogue option in some places but even those are rare. Unless you count the companion quests or that one quest you get from Leliana or Cullen depending on the choices you make in the mage/templar arc. Other than that, cutscenes are mostly reserved for the main campaign.
Edit: Also I forgot about judgements. They have short cutscenes but are also entirely optional for the most part.