Sorry, Tpang - played a couple games with new Inuit and meant to post thoughts. Went to bed first. Note: I played on king and emperor. Here's some quick review:
UA: Much better both in terms of clarity and effect. The main problem with the old Inuit was that you might be keeping up in the culture game, but you couldn't grow your cities - snow was still a killer in terms of building momentum with a city unless you wonderwhored or were on different type of terrain. On the opposite end of the spectrum, the previous effect of gaining culture was in many ways too strong - because if you had at least one city on the snow or tundra, and kept two workers building inuksuks, you could get pretty ridiculous culture outputs with any large amount of tundra/polar tiles. The food bonus is locally-regulated. This is good. The old bonus was empire-wide, and a bit too strong. So the updated ability actually balances in two directions.
Seals nerf is also good, in my opinion. The old production buff was silly. This one works well for if you want to focus down some building or wonder in the early game, buffing the inuit in the early game when they're seriously hurting. It's incredibly difficult to come by early game production in snow or tundra, so the little boost helps. And also having infinite luxury seals resources was a bit strong. So all in all, another good change.
UU: Nerfs! And buffs! Good nerfs here. It becomes basically a slightly more expensive scout that can sacrifice itself to create one kind of improvement. That seems fair. I'd say it's main strength now lies in two things - the incredibly movement ability, and it's ability to upgrade into a composite bow. These two things are balanced out by the range loss, which makes it have to get much closer to engage, and thereby negate at least some of the movement speed, and also the fact that snow and tundra starts have precious few hammers to start with. Making it more expensive production wise makes it slightly less of a good build in comparison with necessities, for example a worker. You cannot survive a snow start without a worker, even as the inuit. If it's a choice between an early worker or an early scout, you're going for the worker. So in terms of build orders, it has also been nerfed. And also, of course, they're nerfed by the fact that early game you'll almost certainly be expending them on fishing boats.
My only wish now would be giving it the ability to walk on ice, as in several games I've had fish tiles separated from me by impassible ice.
UI: Inuksuks are pretty much the same, except that now I believe they work properly.
I kid, but really I haven't encountered bugs with them except for the fact that if you delete one (which should be easier to do, as sometimes you place them wrong), the yields stay and then stack with subsequent inuksuks. This is fairly game-breaking, as you can imagine. As it stands, they make for an absolutely necessary UI on snow, and a pretty fantastic one on tundra. All in all, I believe the Inuit to be true kings and queens of tundra tiles, as they get free Petra for it. They can do very well in snow, but it's still a struggle if you start completely in snow with no fresh water - and especially if you have no sea resources or coast of any kind.
All in all, there might be a couple twinges here and there that would be cool - WALK ON ICE, WALK ON ICE - but other than that, I'd say they're in a good place. The couple bugs that need stomping are few and far between now, and the new icons are AMAZING.