Searching the Minnesota Death Certificates Index found at the Minnesota Historical Society, there is a possible last name found for the mother of some of the children listed in your posted census for FROSLIE:
Birth dates from 1900 census, mother's maiden name from Death Certificates Index:
Selina April 1885 not found
Edwin April 1886 mother's name left blank
Caroline Nov 1887 not found
Joseph Oct 1889 not found
Oliva May 1892 Oliver, same birth date: Johnson
Johonnas Aug 1894 John, same birth date: Johnson
Arthur May 1898 not found
Mother Hanna / Hannah FROSLIE is not found in the index.
*** I should have checked Ancestry.com for a family tree including this family. Olaus E. FROSLIE is listed as marrying Hannah J. MISUNDSTAD.
Sorry I couldn't be of help.