I liked the lockpicking one, except once you got good at it it was too easy to pick locks above your skill. Persuasion was a joke though! Nothing is wrong with a "mini game". Honestly when you first heard we could chop wood, didn't you too think it would have been some sort of mini game?
Chopping wood is turning out like sitting. "you can even sit on a chair or a bench". (player clicks on chair, brief sitting animation plays out, player receives cookie). Lol I'm in no way saying we should have a chair minigame, just that they are both click and watch a short animation.
I think that's the problem with the lockpicking minigame - it's based on a skill, but really depends more on the player's skill/timing. Same thing with persuasion, way too easy even if your speechcraft/personality are low. Minigames in RPGs like these should be heavily and apparently dependent on skills, or they should be not connected to a skill at all. Woodcutting, mining, cooking, farming, and fishing will not have an associated skill, so a minigame might work better for them.
But anyway judging from the behind the scenes video it looks like smithing, enchanting, and alchemy will be recipe systems, with an animation of your player doing the action to make it more interesting. Same will probably go for cooking, but the others just seem like they should be some sort of minigame rather than just clicking to make your player do something while you take a smoke break.
That said when I say "minigame" I'm not talking about some little 2d timing game that cuts away from the action. It needs to be built into the system correctly. If I want to believe that my character has a level 100 security skill I need to see him actually lockpicking.