I'd look for the girls marriage licenses in Otter Tail Co., MN at the County Clerk's office.
An Alfred Nelson married Eva D. Wilson 14 Jan 1914, Kendrick, Latah Co., ID. Volume S, p. 63. Source: brigham Young University Idaho, abish.byui.edu/specialCollections/ .
I didn't find any of the family in 1910 either.
Mathia/Matta died after the 1920 and before the 1930 Census. I looked in the Indaho Death Index and Western States Death Index but didn't find her.
I'd contact the Latah County Historical Society, latah.id.us/historicalsociety/ who does research.
In 1930 Alfred, Eva, children and Halvor were living in Farmington, Latah Co., ID.
Alfred Nelson, b. MN, 38, marr @ 22, diversified farmer.
Eva D., b. WA, 37, marr @ 21.
Harold A., b. ID, 14.
Walter A., b. ID, 12.
Milton A., b. ID, 10.
Mary E., b. ID, 8.
Doris M., b. ID, 6.
Halvor Nelson, b. Norway, 72, father, widower, no occupation.
I didn't find Alfred, Eva or Halvor in the death list but it only goes up to 1951.
I did find a John Nelson living in Trondhjem, Otter Tail Co., MN, 1930 who might be Alfred's brother.
John Nelson, b. MN, 45, both parent's born in Norway.
Lloyd O., 14.
Helma E., 41.