I think I may have found your Arthur and his family of origin:
1930 US Census, Wisconsin, Douglas, Superior, Dist 43 Nelson, Arthur O. Head Rents Value: $500 Male White 38 Married at 29 WI Norway Sweden Dairy Farmer Anna E. Wife 40 Married at 19 Norway Sweden Norway Ruby E. Anderson Stepdaughter 14 WI Norman Nelson Son 9 WI Myrtle E. Nelson Daughter 7 WI Floyd E. Nelson Son 4+ WI Arthur O. Nelson Son 2+ WI
1920 US Census, Wisconsin, Douglas, Superior, Dist 90 Nelson, Oscar Roomer 28 WI Norway Norway (Living in the Larsen Home)
1910 US Census, Wisconsin, Douglas, Superior Ward 9, Dist 104 Nelson, Anna Head 49 Widow 5 born 4 living Sweden Sweden Sweden Engval Son 14 WI Oscar Son 16 WI Laborer Odd Jobs
1905 Wisconsin State Census, Douglas, Superior Nelson, Edward Father 45 Born Norway Parents Born Norway Nelson, Anna Mother 44 Born Born Swed Parents Born Swed Nelson, Hilda Daughter 19 Born Norw Paretns Born Nor/Swed Nelson, Ella Daughter 16 Born WI Nelson, Mary Daughter 14 Born WI Nelson, Art Son 11 Born WI Nelson, Ingvald Son 10 Born WI
1900 US Census, Wisconsin, Douglas, Superior Ward 9, Dist 78 Nelson, Ed Head Aug 1860 39 married 15 years Nor Nor Nor Laborer Annie Wife Mar 1861 39 5 born 5 living Swed Swed Swed Hilda Daughter Sep 1885 14 Norway Ella Daughter Apr 1890 10 WI Olivia (Mary) Daughter June 1891 8 WI Art Son Aug 1893 6 WI Engwald Son Aug 1895 4 WI
Arthur's WW1 Draft Registration lists his birthdate as August 27, 1892, born Superior, WI and his mother is his dependent.
Based on the age of Arthur's eldest child, it is safe to assume that Arthur was married sometime between 1920-1922.I note that his stepdaughter Ruby was born in Wisconsin and that all subsequent children were also born in Wisconsin.Are you positive that he was married in Minnesota?If so, you may want to check Duluth's vital records.
Edward and Annie (Arthur's parents) were married somewhere in Norway as is proved by the place of birth for their eldest child Hilda in 1885.The birth of their second child Ella in Wisconsin in 1890, places their date of immigration from 1886-1890.
I hope you find this information helpful.I certainly with you the very best of luck with your continued research.