The spelling of UINTA(H) — in the 1800s the H was sometimes used and sometimes left off. John Wesley Powell left it off when he spelled the word as part of his 1869 expedition, because he said it was unnecessary for pronunciation of the word.
The U.S. government standardized the spelling later in the 1800s by setting the rule that Uinta without the H would be used for natural features such as the Uinta Mountains or Uinta Basin, and Uintah with the H would be used for man-made entities such as Uintah School or Uintah County. So that is why the school name has the H in it.
So why was the sign above the main door of Uintah School misspelled by leaving off the H? I don’t think it’s known for sure, but it probably involves one of these reasons: (1) In 1915 when the school was built, the spelling guidelines from the government were still so recent that there may still have been some confusion on the issue; (2) The contractor who made the sign might have simply left off the H by mistake, or ran out of room on the cement slab by spacing the letters too far apart and having no room at the end for the H. It might just be that simple.
Thank you to Phillip Snow for his research on the spelling of Uinta(h). This gentleman was also the one who was able to save this piece of history!