Anything by Vilhjálmur Stefánsson.
Amazon.com: Vilhjálmur Stefánsson
My Life with the Eskimo in particular is very good.
It's anthropology rather than history, but if that's of interest he's surely one of the most perceptive observers to have lived with these people. Stefánsson seems to me to have been something of a genius.
I don't honestly know if anyone has written a comprehensive history of how their culture has changed over time and specifically under the impact of modernity. I'd think so, but I don't know whom.
There's probably stuff of interest in Barry Lopez's book, but I have to confess to never being able to get very far with it:
Amazon.com: Arctic Dreams (9780375727481): Barry Lopez: Books
On the food, Weston Price is worth a look:
Nutrition and Physical Degeneration: Chapter 5
Kabloona is probably worth a read:
Amazon.com: Kabloona: Among the Inuit (Graywolf Rediscovery) (9781555972493): Gontran De Poncins, Lewis Galantiere: Books
The blurb is somewhat misleading:
In point of fact, while Gontran de Poncins does get perspective on his own impatience -- preeminently a vice of civilization as Evelyn Waugh remarked in Remote People -- and comes to see that what looks like theft is more a pooling of resources, I don't think he loses perspective on the culture and it's a romanticization to think (a) that he does and (b) that if he had would be a positive thing.He is at first appalled by their way of life: eating rotten raw fish, sleeping with each others wives, ignoring schedules, and helping themselves to his possessions. But as de Poncins odyssey continues, he is transformed from Kabloona, The White Man, an uncomprehending outsider, to someone who finds himself living, for a few short months, as Inuk: a man, preeminently.
It's important to note that in the latter part of the book he's not only more used to the way of life but moving among people who are closer to their traditional way of life, not stuck between two different cultures, and this makes a difference. Furthermore, I doubt Poncins comes to "comprehend" the excessive brutality of the men to their dogs (and even, one's sorry to say, to their wives) or the occasional but not rare resort of individuals to homicide, which happened for a variety of reasons, d=isputes over women, fear of sorcery, and other and stranger reasons. Neither does Poncins accept, or appear to condone, "sexual hospitality" at any point in the book, although he's honest enough to admit to being tempted by it.
It would truer to say that while he doesn't lose perspective on his hosts in time he comes to see their virtues and appreciate their skills. Stefánsson is much faster to do so.