SOURCE: Coldwater, Ohio At 150 (A history book from 1988)
"Soon after the implementation of a 1937 study on Mercer County school district reorganization, Butler Township, Dahlinghaus Special, and parts of Franzer-Uppenkamp and Oakland districts became parts of the Coldwater district. In 1946, Part of Burntwood district became part of Coldwater district, with the larger remainder going to Celina. In 1950, Part of Washington Township District joined Coldwater, and in 1958, Philothea Local became part of Coldwater. In 1958, also, a corridor of land to the west was transferred out of the newly formed Southwest Local School District to Coldwater which enabled St. Anthony (Combined in 1937 with Loughridge) to join Coldwater in that same year."
Lots of school districts that I've never heard of. A few I'm assuming are groups of 1 room schoolhouses. But that in a nutshell says how the Coldwater district, as weirdly shaped as it is, came to be.
Oh and for those outside the area, Southwest local is Fort Recovery.