I have brought up the infamous 1880-81 & 1881-82 winters many times.
They were actually during a period locally which lasted from 1874-75 thru 1881-82 where every other winter alternated from abnormally cold between abnormally warm. Incredibly all 8 of those winters (4 warm, 4 cold) are still in Detroits all-time top 20 coldest/warmest winters list.
The winter of 1880-81 saw 93.6" of snow and an avg temp of 21.6F followed by 1881-82 with 13.2" of snow and a mean temp of 36.9F. There appear to be some errors in snow data earlier than 1885 (id have to go to DTX and look at the archaic books to find out) as xmacis would have the snowfall at 79.4" & 11.5", but regardless, massive difference.
The Laura Ingalls Wilder book, "The Long Winter", while admittedly a bit embellished, is a fascinating read which takes place from late summer 1880 thru spring 1881 in what is now North Dakota. https://en.wikipedia.org/wiki/The_Long_Winter_(novel)
The following book, "Little Town on the Prairie", while not specifically weather focused, discusses the extraordinarily mild winter 1881-82 in Dakota. https://en.wikipedia.org/wiki/Little_Town_on_the_Prairie
Daily newspapers accounts also talked about the harshness of the 1880-81 winter and the remarkably mild 1881-82 winter.