Wayne,
I don't have a 'for sure' answer for you but from what I can tell, everyone was enumerated, even in the northern reserves. I doubt that families kept their own records, anymore than they do today. Do you have an approx. year of birth?

I'm don't know where Split Lake is but could this be her family?
Thomas MOOSE M Male Indigenous 65 Northwest Territories Hunter Weslyan Methodist
Sarah MOOSE M Female Indigenous 60 Northwest Territories Weslyan Methodist
Anne MOOSE M Female Indigenous 45 Northwest Territories Weslyan Methodist
Charles MOOSE Male Indigenous 23 Northwest Territories Hunter Weslyan Methodist
Henry MOOSE Male Indigenous 20 Northwest Territories Hunter Weslyan Methodist
William MOOSE Male Indigenous 17 Northwest Territories Hunter Weslyan Methodist
Andrew MOOSE Male Indigenous 16 Northwest Territories Weslyan Methodist
Mary MOOSE Female Indigenous 14 Northwest Territories Weslyan Methodist
James MOOSE Male Indigenous 14 Northwest Territories Weslyan Methodist
Thomas MOOSE Male Indigenous 12 Northwest Territories Weslyan Methodist
Jane MOOSE Female Indigenous 11 Northwest Territories Weslyan Methodist
Source Information:
Census Place Lake Winnipeg, North Eastern Extension, Extension, Manitoba
Family History Library Film 1375920
NA Film Number C-13284
District 186
Sub-district C
Page Number 33
Household Number 145