This isn't your answer - but it might help. His wife was Elizabeth Neufauer or Neubauer - from the records on George's siblings - you might have better luck with the handwriting - and she was from Germany as well. Maybe you can find their marriage record? It appears that Andrew died sometime between 1886 and 1892 - as last child was born May 1877 and maybe 1892 - when 'Lizzie' is living with all 6 children - but no Andrew. Doesn't specify widow on that census, but 1900 does. So another possibility is finding his death record is Ostego, NY in that timeframe - I didn't find it online? Some records below, links will bring you to those records or images. Not all would fit here. Good Luck
U S Census, 1880 Cooperstown, Otsego, New York
Citing this Record "United States Census, 1880," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MZF3-CDR
Self Andrew Schneider M 31 GER
Wife Lizzie Schneider F 29 GER
Son John Schneider M 5 NY
Dau Emma Schneider F 2 NY
Son George Schneider M 1 NY
New York, County Marriages, 1908-1935
Image Source: https://familysearch.org/pal:/MM9.3.1/TH-1-159371-172248-70?cc=1618491&wc=M9Q9-YHT:687237422
Marriage License: Jan. 15, 1912
John Schneider
Residence: Cooperstown Occupation Tailor
Age: 36 White Single
Birth (Est) 1876 Birthplace: Cooperstown
Father Andrew Schneider Birthplace Germany
Mother Elizabeth Neufouer Birthplace Germany
Spouse's Name: Mary E Kraham
Residence Cooperstown Occupation Domestic
Age: 41 White Single
Birth Year (Est) 1871 Birthplace Middlefield
Father James Kraham Birthplace Ireland
Mother Bridget Weisse Birthplace Ireland
Digital Folder Number: 004489584
Image Number: 00454
Marriage Record: Jan. 16, 1912
Image Source: https://familysearch.org/pal:/MM9.3.1/TH-1-159366-20762-68?cc=1618491&wc=M9Q9-Y4N:334850005
Image Source: https://familysearch.org/pal:/MM9.3.1/TH-1-159366-20855-72?cc=1618491&wc=M9Q9-Y4N:334850005
Bernard F Jeffrey
Marriage 25 Sep 1912 Otsego, NY
Age: 30 Birth (Est) 1882 Red Bank, NJ
Father Jacob Jeffrey USA
Mother Anna Fryer USA
Spouse Katherine E Schneider
Age: 30 Birth (Est) 1882 Cooperstown
Father Andrew Schneider GER
Mother Elizabeth Newbower GER
Image Number: 00164
New York, State Census, 1875 ED 01 Ostego, Ostego, NY
Citing this Record "New York, State Census, 1875," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/VNKH-L5L
Andrew Snyder M 27 GER Tailor
Wife Eliza Snyder F 25 GER
Son John Snyder M 0 (? 4 mos) Ostego
U S Census, 1900 ED 134 Otsego Township Cooperstown village, Otsego, NY
Citing this Record "United States Census, 1900," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MSLD-44N
Head Elizabeth Schneider F 50 June 1850 GER Widow 6 children 6 living immig ABT 1875
Son John Schneider M 25 Feb 1875 NY
Dau Emma Schneider F 23 J? an or June 1877 NY
Son George Schneider M 22 Sept 1878 NY
Dau Katie Schneider F 20 July 1880 NY
Son Charles A Schneider M 16 April 1884 NY
Dau Dora E Schneider F 13 May 1887 NY
New York, State Census, 1892 Otsego, E.D. 03, Ostego, NY
Image Source: https://familysearch.org/pal:/MM9.3.1/TH-267-11689-92949-32?cc=1529100&wc=10935379
Lizzie is living with above children, no Andrew in household
