What are the butterfly effects here? You seem to be looking exclusively at the inuit but the potential here far surpasses them. Domestication of caribou and musk-ox, in a rapidly spreading culture? Come on now, its obvious the rest of at least North America is going to pick up on this, starting likely are the Inuit have spread south somewhat the trick will rapidly move through OTL's Quebec, Ontario, and the Northeast US. That's going to have massive butterfly effects.
EDIT: And what about disease? Domestication breeds disease, which means the Inuit and other northern natives now have at least potentially one biological weapon of their own for when the Europeans show up. That alone will have its own, huge, set of butterflies to deal with.
Having these discussions. Among other things, there are going to be huge butterflies handicapping the British (but not necessarily the French fur trade).
In terms of domestication issues, I'm not sure that domesticating caribou will spread. You might see it with the Dene. Or you might see the Dene overrun.
Move south past the Dene, and you've got the swampy cree. Not good caribou territory. Moose country actually. But the Swampy Cree are riverine people, their lifestyle was such that they never domesticated moose for the same reason that the Inuit didn't domesticate caribou. Partly, didn't need to, and partly, the animal's life cycle was incompatible with their cultural economics.
Another thing is if you look at the precedent of Reindeer domestication with the lapplanders, that only goes back about 500 years, and it seems to have had something to do with territorial encroachment by the Norwegians. The Lapps, prior to that, simply followed the herds or hunted seasonally, and saw no real interest. So, there was something that happened to the people/territory equation that shifted things over. I think we've got a comparable mechanism for the Inuit, but I'm not persuaded that the mechanism would kick in for southern cultures.
As for the rest of the agricultural package, I'm somewhat cautious on how far south it would effectively extend, and the degree that cultures like the Swampy Cree or the Dene would pick it up.
In terms of disease issues, we've got an argument going on, on that score right now. I'm not inclined to think that Musk Ox are going to pose much of a problem - they'll be more victims than vectors - low population densities and sedentary habits. Caribou are riskier, highly mobile herds and high population densities. But even there, there's issues in degree of risk assessment.
But even if, for instance, you don't have widespread domestication/agriculture/diseases spreading to cultures south of the inuit, there's going to be at least two classes of butterflies which will shake up the south.