I do not find him in the 1890 Census of Civil War Veterans and Widows for Lawrence County. There is no 1890 Population census for Lawrence County and most of the rest of the US. I did find the following biographical sketch which contains a lot of valuable family information. However these biographies are not always accurate and the information should be verified from other sources. According to the biography he was in Gilbertville, Iowa, in 1870 and 1880.
"Matthias MUELLER was born at Banstert, in Rhine Province, Prussia, June 9, 1829, and is the son of Matthias and Margaretha (AMBROSE) MUELLER, of the better class of yeomanry of that Burgemertrie. Matthias Mueller, Jr., completed a good trade at shoemaking, served two years, and then worked at his master-piece in a Government shop, and received a creditable diploma. In 1854 he turned his face toward the American continent, embarking at Antwerp he landed in New York City May 15 of the same year. He went immediately to Buffalo, and in March, 1855, moved to Illinois, where he made a location near Naperville. In the fall he went to Michigan, and after spending some time there he returned to New York State. In the fall of 1857 he went back to Illinois with his parents, a brother and two sisters, whom he had brought over from the old country, and located in Naperville. Here he worked at his trade for about two years, after which he sold out and worked in Will County, Ill., near Lockport, until the beginning of the war. In the spring of 1862 he engaged in mining, and followed this until July, when he returned to Illinois, and followed shoemaking at Naperville, until he lost the use of his right hand first finger, when he returned to farming. He then went to Michigan, but his health not being good here he returned to Illinois, where, on account of his health, he was obliged to abandon shoemaking. He farmed there until 1867, when he moved to Iowa, and in the fall of 1868 he located at Gilbertville, Iowa, where he engaged in mercantile pursuits. This occupation he carried on for fifteen years and was also postmaster at the same place for the same length of time. On account of his health he sold out and moved to Lawrence County, Mo., in 1884, and here he has since remained. He purchased a farm in Barry County, and has kept hotel nearly ever since. He was married in New York in 1855 to Miss Mary GASPAR, who was a native of Germany, and the daughter of John and Johanna (KLEIN) GASPAR. Mr. and Mrs. Mueller have reared four sons and three daughters: Margaret (wife of Thomas GILLEY, a leading merchant of Waterloo, Iowa), John W. (at Verona, Mo.), Mary Maria (at home), Katrina (wife of Frederick PRUENTY, of St. Louis), Christian (at home) and William (at home). Mr. and Mrs. Mueller and all their children are regular communicants of the Roman Catholic Church. Mr. Mueller has 320 acres of well-improved land, the Cassville road running through his land and cutting it into quarter sections. He has good buildings, orchards, and has some fine Short-horn cattle."
From "A Reprint of Goodspeed's 1888 History of Lawrence County; Reprint Lawrence County Section of Goodspeed's Newton, Lawrence, Barry And McDonald Counties History; published by the Goodspeed Publishing Co., in 1888; Reprinted by Litho Printers Of Cassville, Missouri In 1973." as transcribed by Judy Johnson Reustle, p. 233.
I did not an obituary for he or his widow. I did find a reference to a Probate file for Mathias Miller (Mueller spelled phonetically as you probably know) in Feb. 1895. It is in box 52, file 1194. You may contact the Probate Court at the Courthouse in Mount Vernon to see about getting a photocopy of the file.