Never, ever heard any Inuit refer to or even accept the term Indian or First Nations applied to themselves.History, the term "Indian" did apply to and include the Inuit, and is synonymous with the term "aboriginal peoples" according to the Supreme Court of Canada:
Daniels v. Canada (Indian Affairs and Northern Development), 2016 SCC 12 (CanLII), [2016] 1 SCR 99