Hi.I'm not related to this family.The first thing you should know is that Conrad came from Russia, not Prussia.Here he is in 1900:
1900 United States Federal Census about Konrad Winters Name: Konrad Winters [Konrad Winter] Age: 39 Birth Date: Jul 1860 Birthplace: Russia Home in 1900: Cedron, Lincoln, Kansas [Hanover, Lincoln, Kansas] Race: White Gender: Male Immigration Year: 1893 Relation to Head of House: Head Marital Status: Married Spouse's Name: Mollie Winters Marriage Year: 1893 Years Married: 7 Father's Birthplace: Russia Mother's Birthplace: Russia Household Members: Name Age Konrad Winters 39b. Jul 1860 Russia, parents b. Russia; immigration 1893; Farmer Mollie Winters 35 -wife- b. Jun 1864 Russia, par b. Russia; imm 1893; married 7 years; 4 children/4 surviving George Winters 7 -son- b. Apr 1893 Kansas Caroline Winters 4 -dau- b. Dec 1895 Kansas Mollie Winters3 -dau- b. May 1897 Kansas Fred Winters 1 -son- b. Dec 1898 Kansas Fred Winters 29 -nephew- b. Nov 1870 Russia, par b. Russia; immigration 1898; farmer
There is a reference to a Carl Conrad Winter emigrating in 1892:
Passenger and Immigration Lists Index, 1500s-1900s about Carl Conrad Winter Name: Carl Conrad Winter Year: 1892 Age: 37 Estimated Birth Year: abt 1855 Place: Kansas Source Publication Code: 3435.55 Primary Immigrant: Winter, Carl Conrad Annotation: Date and place of declaration of intention or naturalization. Country of nativity and volume and page number reference to original record are also provided. Source Bibliography: INDEX TO NATURALIZATION RECORDS OF SHAWNEE COUNTY, KANSAS 1865-1930. Topeka: Topeka Genealogical Society, 1992. 81p. Page: 80
In the 1910 & 1920 Census the family is living in Lehigh, Kansas with an immigration date of 1891, and the couple is listed as being born in "Russ-German" in 1910 and "Central Russia" native language "German" in 1920.There is also a naturalization date of 1918 (or naturalized 1914 in the 1925 census).
Sorry I couldn't find them on a ship's list.According to a tree on Ancestry.com, Conrad Winter was born 16 JUN 1861 in Shcherbakovka, Russia and died 5 Jun 1945 in Hillsboro, Kansas. Hope this helps.Annie