Hi,
I don't know where you'll find a written history of Schulter. I'd check with Ruby Wesson at the Henryetta Library first. That's only five or seven miles south of Schulter. Then there's the Okmulgee Library, probably ten miles north of S.
I'm guessing the town came into being between the 1910 and 1920 censuses, because of the coal mines and the oil wells discovered there.
Do let me know if you find anything out--I'm interested, too.
Ginger